Shiing-Shen Chern | Academic Influence

Shiing-Shen Chern's AcademicInfluence.com Rankings

Shiing-Shen Chern

Mathematics

#22

World Rank

#78

Historical Rank

Differential Geometry

#2

World Rank

#5

Historical Rank

Geometry

#7

World Rank

#15

Historical Rank

Measure Theory

#165

World Rank

#251

Historical Rank

mathematics Degrees

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Mathematics

Shiing-Shen Chern's Degrees

PhD Mathematics University of Hamburg

Why Is Shiing-Shen Chern Influential?

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According to Wikipedia, Shiing-Shen Chern was a Chinese-American mathematician and poet. He made fundamental contributions to differential geometry and topology. He has been called the "father of modern differential geometry" and is widely regarded as a leader in geometry and one of the greatest mathematicians of the twentieth century, winning numerous awards and recognition including the Wolf Prize and the inaugural Shaw Prize. In memory of Shiing-Shen Chern, the International Mathematical Union established the Chern Medal in 2010 to recognize "an individual whose accomplishments warrant the highest level of recognition for outstanding achievements in the field of mathematics".

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Shiing-Shen Chern's Published Works

Number of citations in a given year to any of this author's works

Total number of citations to an author for the works they published in a given year. This highlights publication of the most important work(s) by the author

Published Works

An Introduction to Riemann-Finsler Geometry (2000) (1816)
Characteristic forms and geometric invariants (1974) (895)
Differential Geometry: Cartan's Generalization of Klein's Erlangen Program (2000) (647)
Minimal Submanifolds of a Sphere with Second Fundamental Form of Constant Length (1970) (600)
Minimal Submanifolds of a Sphere with Second Fundamental Form of Constant Length (1970) (600)
Real hypersurfaces in complex manifolds (1974) (564)
Riemann-Finsler geometry (2005) (533)
Exterior Differential Systems (1990) (435)
The Theory Of Lie Derivatives And Its Applications (1959) (428)
Complex manifolds without potential theory (1979) (421)
A simple instrinsic proof of the Gauss Bonnet formula for closed Riemannian manifolds (1944) (399)
On the Total Curvature of Immersed Manifolds (1957) (310)
Hermitian vector bundles and the equidistribution of the zeroes of their holomorphic sections (1965) (302)
Characteristic Classes of Hermitian Manifolds (1946) (267)
Lectures On Differential Geometry (1981) (206)
Minimal surfaces by moving frames (1983) (200)
On Finsler geometry (1992) (200)
Some Theorems on the Isometric Imbedding of Compact Riemann Manifolds in Euclidean Space (1952) (184)
An elementary proof of the existence of isothermal parameters on a surface (1955) (183)
Complete minimal surfaces in Euclideann-space (1967) (176)
Pseudospherical surfaces and evolution equations (1986) (171)
Differentiable Manifolds: Forms, Currents, Harmonic Forms (1984) (166)
On the Curvatura Integra in a Riemannian Manifold (1945) (160)
The geometry of $G$-structures (1966) (160)
Minimal submanifolds in a Riemannian manifold (1968) (156)
Finsler Geometry Is Just Riemannian Geometry without the Quadratic Restriction (1997) (150)
Harmonic maps of the two-sphere into a complex Grassmann manifold II* (1987) (142)
On the index of a fibered manifold (1957) (132)
On riemannian metrics adapted to three-dimensional contact manifolds (1985) (128)
Some cohomology classes in principal fiber bundles and their application to riemannian geometry. (1971) (127)
On Curvature and Characteristic Classes of a Riemann Manifold (1955) (124)
On the curvatures of a piece of hypersurface in euclidean space (1965) (104)
On the total curvature of immersed manifolds. II. (1958) (102)
ON A NOTABLE CONNECTION IN FINSLER GEOMETRY (1996) (99)
Intrinsic norms on a complex manifold (1996) (98)
An analogue of Bäcklund's theorem in affine geometry (1980) (92)
Minimal Surfaces in an Euclidean Space of N Dimensions (1965) (79)
On the Kinematic Formula in Integral Geometry (1966) (79)
Sur la Géométrie d’un Système d’Équations Différentielles du Second Ordre (1989) (76)
Abel's Theorem and Webs. (1978) (74)
Review: Luis A. Santaló, Integral geometry and geometric probability (1977) (73)
Deformation of Surfaces Preserving Principal Curvatures (1985) (73)
Curves and surfaces in Euclidean space (1967) (72)
On the Multiplication in the Characteristic Ring of a Sphere Bundle (1948) (72)
On the Volume Decreasing Property of a Class of Real Harmonic Mappings (1975) (69)
Some new characterizations of the Euclidean sphere (1945) (69)
A note on the Gauss-Bonnet theorem for Finsler spaces (1996) (62)
Local Equivalence and Euclidean Connections in Finsler Spaces (1989) (60)
A theorem on orientable surfaces in four-dimensional space (1951) (59)
Integral Formulas for Hypersurfaces in Euclidean Space and Their Applications to Uniqueness Theorems (1959) (56)
Studies in global geometry and analysis (1968) (55)
Lie groups and KdV equations (1979) (54)
Topics in differential geometry (1951) (54)
Dupin submanifolds in lie sphere geometry (1989) (51)
What is geometry (1990) (51)
On the Kinematic Formula in the Euclidean Space of N Dimensions (1952) (51)
Classical Chern-simons Theory, Part 2 (1993) (51)
COMPLEX ANALYTIC MAPPINGS OF RIEMANN SURFACES I. (1960) (50)
On Integral Geometry in Klein Spaces (1942) (49)
On special $W$-surfaces (1955) (48)
BRACKETS, FORMS AND INVARIANT FUNCTIONALS (2005) (45)
Eine Invariantentheorie der Dreigewebe aus r- dimensionalen Mannigfaltigkeiten imR2r (1935) (43)
On a Generalization of Kähler Geometry (1957) (43)
Tautness and Lie sphere geometry (1987) (43)
On the projective structure of a real hypersurface in C... (1975) (43)
Élie Cartan and his mathematical work (1952) (42)
The Integrated form of the First Main Theorem for Complex Analytic Mappings in Several Complex Variables (1960) (39)
Foliations on a surface of constant curvature and the modified Korteweg-de Vries equations (1981) (39)
Algebraic Geometry and Topology . A symposium in honor of S. Lefschetz. R. H. Fox, D. C. Spencer, A. W. Tucker, Eds. Princeton University Press, Princeton, N.J., 1957. 408 pp. $7.50. (1957) (39)
On surfaces of constant mean curvature in a three-dimensional space of constant curvature (1983) (39)
On the Euclidean Connections in a Finsler Space. (1943) (38)
Einstein hypersurfaces in a Kählerian manifold of constant holomorphic curvature (1967) (35)
On the Characteristic Classes of Complex Sphere Bundles and Algebraic Varieties (1953) (35)
Geometrical interpretation of the sinh-Gordon equation (1981) (31)
CURVATURE AND GLOBAL RIGIDITY IN FINSLER MANIFOLDS (2002) (30)
Complex Manifolds without Potential Theory: with an appendix on the geometry of characteristic classes (1995) (28)
Global differential geometry (1991) (28)
Lecture note on differential geometry (1951) (27)
Sur la Géométrie d’une Équation Différentielle du Troisième Ordre (1989) (27)
An inequality for the rank of a web and webs of maximum rank (1978) (27)
Riemannian geometry in an orthogonal frame : from lectures delivered by Élie Cartan at th Sorbonne in 1926-27 (2001) (27)
Surface Theory with Darboux and Bianchi (1991) (27)
Tight and Taut Submanifolds (2011) (26)
Groupes et géométries de Coxeter (2001) (26)
ON THE RIEMANN MAPPING THEOREM (1996) (25)
On the projective structure of a real hypersurface in $\mathsf{C}_{n+1}$. (1975) (24)
Abzählungen für Gewebe (1935) (23)
Seminar on nonlinear partial differential equations (1984) (23)
From Triangles to Manifolds (1979) (23)
The Homology Structure of Sphere Bundles. (1950) (22)
Contemporary Trends in Algebraic Geometry and Algebraic Topology (2002) (22)
Differential Geometry of Fiber Bundles (1989) (21)
Projective geometry and Riemann's mapping problem (1995) (20)
Historical Remarks on Gauss-Bonnet (1990) (20)
Some new viewpoints in differential geometry in the large (1946) (20)
La Géométrie des Sous-Variétés d’un Espace Euclidien a Plusieurs Dimensions (1989) (19)
MINIMAL IMMERSIONS OF SPHERES INTO SPHERES (19)
Remarks on the Riemannian metric of a minimal submanifold (1981) (17)
S. S. Chern : a great geometer of the twentieth century (1992) (17)
Harmonic maps of S into a complex Grassmann manifold. (1985) (15)
Selected Papers II (1989) (15)
A Proof of the Uniqueness of Minkowski's Problem for Convex Surfaces (1957) (15)
Linear Differential Systems (1991) (13)
Exterior Differential Calculus (1999) (13)
Vector Bundles with a Connection (1989) (13)
Laplace Transforms of a Class of Higher Dimensional Varieties in a Projective Space of n Dimensions. (1944) (12)
Differential Geometry in Symplectic Space I (1989) (12)
On the isometry of compact submanifolds in euclidean space (1963) (11)
Finsler Geometry: Joint Summer Research Conference on Finsler Geometry, July 16-20, 1995, Seattle, Washington (1996) (11)
Some Formulas Related to Complex Transgression (1970) (10)
Integral Formulas for the Characteristic Classes of Sphere Bundles. (1944) (10)
Geometry of a Quadratic Differential Form (1962) (10)
Jean-Pierre Serre (2001) (10)
Differential Geometry and Integral Geometry (1989) (9)
A Generalization of the Projective Geometry of Linear Spaces. (1943) (9)
On A Conformal Invariant of Three-Dimensional Manifolds (1986) (9)
from the Generalized Schur Algorithm (1994) (8)
On the Characteristic Classes of Riemannian Manifolds. (1947) (8)
DIFFERENTIAL GEOMETRY ; ITS PAST AND ITS FUTURE by (2010) (8)
AN INTRODUCTION TO DUPIN SUBMANIFOLDS (1996) (8)
My Mathematical Education (1996) (7)
Review: Jerry L. Kazdan, Prescribing the curvature of a Riemannian manifold (1987) (7)
Lectures on integral geometry (1965) (7)
The imbedding theorem for fibre bundles (1949) (7)
A Simple Proof of Frobenius Theorem (1981) (6)
A Uniqueness Theorem on Closed Convex Hypersurfaces in Euclidean Space (1960) (6)
Support Theorems for Horocycles on Hyperbolic Spaces (2012) (6)
On Riemannian manifolds of four dimensions (1945) (5)
The Geometry of Isotropic Surfaces (1942) (5)
Linearizing Flows and a Cohomology Interpretation of Lax Equations (1984) (5)
Scientific report on the second summer institute, several complex variables. Part II. Complex manifolds (1956) (5)
Erratum to: Real hypersurfaces in complex manifolds (1983) (5)
The mathematical works of Wilhelm Blaschke (1973) (4)
Differential Geometry, Part 2 (1975) (4)
Projective geometry, contact transformations, andCR-structures (1982) (4)
A Summary of My Scientific Life and Works (1996) (4)
Finsler Metrics of Scalar Flag Curvature (2005) (3)
Projectively Flat Finsler Metrics (2005) (3)
Duality properties of characteristic forms (1976) (3)
The collected papers of Wei-Liang Chow (2002) (3)
Review: A. Lichnerowicz, Théorie globale des connexions et des groupes d'holonomie (1957) (3)
Topologische Fragen der Differentialgeometrie 60 (1996) (3)
Wolf prize in mathematics (2000) (3)
Lars Valerian Ahlfors (2000) (2)
Note on affinely connected manifolds (1947) (2)
TRANSGRESSION IN ASSOCIATED BUNDLES (1991) (2)
Relations between Riemannian and Hermitian geometries (1953) (2)
Associate Quadratic Complexes of a Rectilinear Congruence (1989) (2)
New developments in the theory of geometric partial differential equations (1986) (2)
Physics And Mathematics of Anyons: Proceedings of the TCSUH Worshop (1991) (2)
Remarks on hibert’s 23rd problem (1996) (2)
Sur les Invariants Intégraux en Géométrie (1989) (2)
Shiing-Shen Chern : a great mathematician of the twentieth century (2006) (2)
Differentiable manifolds : 354a notes (1953) (2)
Yang-Mills Equations and Yang-Baxter Equation (1996) (2)
Proceedings of the 1980 Beijing Symposium on Differential Geometry and Differential Equations = [1980 nien "shuang wei" Pei-ching tʿao lun hui wen chi] (1982) (1)
Mark Grigor'evich Krein (1990) (1)
Pairs of Plane Curves with Points in One-to-One Correspondence (1989) (1)
Review: A. Weil, Variétés abéliennes et courbes algébriques (1950) (1)
Parallelisability of principal fibre bundles (1949) (1)
The Chern Connection (2000) (1)
Sophus Lie and diffferential geometry (1996) (1)
Joseph B. Keller (2000) (1)
WEI-LIANG CHOW, 1911–1995 (2002) (1)
Sheaves and Cohomology (1979) (1)
Proceedings of the thirteenth biennial seminar of the Canadian Mathematical Congress on Differential topology ; Differential geometry and applications (1972) (1)
Applications of Commutative Algebra and Algebraic Geometry to the Study of Exterior Differential Systems (1991) (1)
SHIING-SHEN CHERN: 1911–2004 (2008) (1)
CHARACTERISTIC CLASSES AS A GEOMETRIC OBJECT (1996) (1)
Holomorphic Vector Bundles and Line Bundles (1979) (1)
Selected Papers IV (1989) (1)
The Grassmann Manifold (1979) (1)
General Relativity and Differential Geometry (1980) (1)
S. S. Chern and Chern-Simons Terms ∗ (2005) (1)
Review: W. T. Wu and G. Reeb, Sur les espaces fibrés et les variétés feuilletées (1953) (0)
Carl L. Siegel (2001) (0)
Complex Vector Bundles; Connections (1979) (0)
Open Discussion: E. Amaldi, Chairman (1980) (0)
Geschichte des mannigfaltigkeitsbegriffs von riemann bis poincaré: By Erhard Scholz. Boston (Birkhauser). 1980. 430 pp (1984) (0)
Les hypersurfaces dans l'espace euclidien (1960) (0)
On a Weyl Geometry Defined from an (n - 1) Parameter Family of Hypersurfaces in a Space of n Dimensions (1989) (0)
Sur une Généralisation d’une Formule de Crofton (1989) (0)
Sur les Invariants de Contact en Géométrie Projective Différentielle (1989) (0)
Sur les métriques riemanniennes compatibles avec une réduction du groupe structural (1960) (0)
Lie Groups and Moving Frames (1999) (0)
"little more than a plaything". The issue was forced by Bertrand's paradox, which arose from the fact that the measure is not unique for geometric events (2007) (0)
Almost Complex Manifolds; Integrability Conditions (1979) (0)
Cartan-Kähler Theory (1991) (0)
Shiing-Shen Chern (2000) (0)
A Tribute to Herrn Erich Kähler (2003) (0)
Partial differential equations : proceedings of a symposium held in Tianjin, June 23-July 5, 1986 (1988) (0)
Review: F. Hirzebruch, Neue topologische Methoden in der algebraischen Geometrie (1958) (0)
Proceedings of the 1983 Beijing Symposium on Differential Geometry and Differential Equations = 1983年"双微"北京討論会文集 (1986) (0)
The Characteristic Variety (1991) (0)
Peter D. Lax (2001) (0)
Andrei N. Kolmogorov (2001) (0)
Differential Geometry, Part 1 (1975) (0)
Pao-Lu Hsu (Xu, Bao-lu): The Grandparent of Probability and Statistics in China (2012) (0)
The Life and Mathematics of Shiing-Shen Chern (2006) (0)
Curvature and Schur’s Lemma (2000) (0)
The Index Form and the Bonnet—Myers Theorem (2000) (0)
Hermitian Geometry and Kählerian Geometry (1979) (0)
Jürgen K. Moser (2001) (0)
I Results in Mathematics Isospectrality for Spherical Space Forms (2013) (0)
Curves in a Grassmann Manifold (1979) (0)
Proceedings of the 1982 Changchun Symposium on Differential Geometry and Differential Equations = 1982年"双微"長春討論会文集 (1986) (0)
Andrew J. Wiles (2001) (0)
Finsler Surfaces and a Generalized Gauss-Bonnet Theorem (2000) (0)
list of Chauvenet Prize winners (2013) (0)
Families of Hypersurfaces Under Contact Transformations in Rn (1996) (0)
Wolf Prize in Mathematics: Volume 2 (2001) (0)
INTEGRAL FORAIULAS FOR THE CIIARACTERISTIC CLASSES OF SPIIERE B UNDLES (2005) (0)
Wei-Liang Chow (1997) (0)
Constant Flag Curvature Spaces and Akbar-Zadeh’s Theorem (2000) (0)
There was a total registration of 256 , including the following 206 members of the Society : (2007) (0)
Tight and taut submanifolds : papers in memory of Nicolaas H. Kuiper (1997) (0)
Differential geometry : [proceedings of the Symposium in Pure Mathematics of the American Mathematical Society, held at Stanford University, Stanford, California, July 30-August 17, 1973 (1975) (0)
Kentaro Yano–My Old Friend (1982) (0)
Note on Projective Differential Line Geometry (1989) (0)
On the Bäcklund Transformations of KDV Equations and Modified KDV Equations (1989) (0)
Introduction and Examples (1979) (0)
Shiing-Shen Chern file (1989) (0)
D G ] 3 0 Ju l 2 00 5 η-invariant and flat vector bundles (2008) (0)
Finsler Manifolds and the Fundamentals of Minkowski Norms (2000) (0)
Book Review: Elie Cartan} (1869--1951) (1994) (0)
Randers Spaces and an Elegant Theorem (2000) (0)
On Two Affine Connections (1989) (0)
Wolf Prize in Mathematics: Volume 1 (2000) (0)
Minkowski Spaces, the Theorems of Deicke and Brickell (2000) (0)
EQUIVARIANT MINIMAL IMMERSIONS OFS 2 INTO S 2 m ( l ) (2010) (0)
Review: L. A. Santaló, Introduction to integral geometry (1955) (0)
Complex and Hermitian Structures on a Vector Space (1979) (0)
GAUGE THEORY AT TSINGHUA (2002) (0)
Physics and mathematics of anyons : proceedings of the TCSUH Workshop, Houston, Texas, USA, 1-2 February 1991 (1991) (0)
The Gauss Lemma and the Hopf-Rinow Theorem (2000) (0)
Variations of Arc Length, Jacobi Fields, the Effect of Curvature (2000) (0)
The Cut and Conjugate Loci, and Synge’s Theorem (2000) (0)
John W. Milnor (2001) (0)
Riemannian Manifolds and Two of Hopf’s Theorems (2000) (0)
Variations on Prequantization by Alan Weinstein and Marco Zambon (2005) (0)
Characteristic Classes and Characteristic Forms (1991) (0)
Linear Differential Operators (1991) (0)
Harmonic maps of S2 into a complex Grassmann manifold: (harmonic sequences/Frenet harmonic sequences/fundamental collineations/harmonic flags/”crossing“ and ”turning“ constructions) (1989) (0)
Elias M. Stein (2001) (0)
ON THE CONNECTION IN FINSLER SPACE (2002) (0)
The Cartan—Hadamard Theorem and Rauch’s First Theorem (2000) (0)
On Projective Normal Coordinates (1938) (0)
53–03 Historical (must Also Be Assigned at Least One Classification Number from Section 01) (0)
Extrinsic global differential geometry (1962) (0)
Ilya Piatetski-Shapiro (2001) (0)
Correction to my paper “Note on affinely connected manifolds” (1948) (0)
Yakov G. Sinai (2001) (0)
Berwald Spaces and Szabó’s Theorem for Berwald Surfaces (2000) (0)
DIFFERENTIABLE MANIFOLDS DIFFERENTIAL GEOMETRY OF FIBER BUNDLES (2010) (0)

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