Wilhelm Klingenberg | Academic Influence

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Wilhelm Klingenberg

Mathematics

#1225

World Rank

#2050

Historical Rank

Measure Theory

#1079

World Rank

#1387

Historical Rank

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Mathematics

Wilhelm Klingenberg's Degrees

PhD Mathematics University of Göttingen

Why Is Wilhelm Klingenberg Influential?

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According to Wikipedia, Wilhelm Paul Albert Klingenberg was a German mathematician who worked on differential geometry and in particular on closed geodesics. Life Klingenberg was born in 1924 as the son of a Protestant minister. In 1934 the family moved to Berlin; he joined the Wehrmacht in 1941. After the war, he studied mathematics at the University of Kiel, where he finished his Ph.D. in 1950 with , with a thesis in affine differential geometry.

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Wilhelm Klingenberg'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

Lectures on closed geodesics (1978) (469)
Riemannsche Geometrie im Großen (1975) (307)
A course in differential geometry (1978) (245)
Contributions to Riemannian Geometry in the Large (1959) (150)
Über Riemannsche Mannigfaltigkeiten mit positiver Krümmung (1961) (129)
Riemannian Manifolds With Geodesic Flow of Anosov Type (1974) (127)
Projektive und affine Ebenen mit Nachbarelementen (1954) (121)
Projektive Geometrien mit Homomorphismus (1956) (106)
Generic properties of geodesic flows (1972) (86)
On the envelope of holomorphy of a 2-sphere in ² (1991) (86)
Riemannian Geometry (1982) (85)
Desarguessche Ebenen mit Nachbarelementen (1955) (80)
An Indefinite Kähler Metric on the Space of Oriented Lines (2004) (68)
Lineare Gruppen Uber Lokalen Ringen (1961) (63)
Eine Vorlesung über Differentialgeometrie (1973) (58)
On the Envelope of Holomorphy of a 2-Sphere in ℂ 2 (1991) (57)
Homology generated by iterated closed geodesics (1983) (55)
Symplectic Groups Over Local Rings (1963) (53)
Lineare Algebra und analytische Geometrie (1971) (45)
Orthogonale Gruppen Uber Lokalen Ringen (1961) (41)
ON THE TANGENT SPHERE BUNDLE OF A 2-SPHERE (1975) (37)
On the geometry of spaces of oriented geodesics (2009) (33)
Closed geodesics on Riemannian manifolds (1983) (32)
Geodätischer Fluß auf Mannigfaltigkeiten vom hyperbolischen Typ (1971) (30)
Riemannsche Hilbert-mannigfaltigkeiten : periodische Geodätische (1972) (28)
Euklidische Ebenen mit Nachbarelementen (1954) (28)
Manifolds With Restricted Conjugate Locus: II (1963) (27)
Die Struktur der linearen Gruppe über einem nichtkommutativen lokalen Ring (1962) (25)
Beziehungen zwischen einigen affinen schließungssätzen (1952) (22)
Zur affinen Differentialgeometrie (1951) (21)
Generalised Surfaces in R 3 (2004) (21)
Über Riemannsche Mannigfaltigkeiten mit nach oben beschränkter Krümmung (1962) (21)
FLOW OF REAL HYPERSURFACES BY THE TRACE OF THE LEVI FORM (1999) (20)
Lineare Algebra und Geometrie (1984) (19)
Injectivity radius estimate for 1/4-pinched manifolds (1980) (19)
Zur affinen Differentialgeometrie: Teil I: berp-dimensionale Minimalflchen und Sphren imn-dimensionalen Raum (1951) (18)
Linear groups over local rings (1960) (17)
Über SeiteneinteiIungen in affinen und euklidischen Ebenen (1951) (16)
Proof of the Caratheodory Conjecture (2008) (16)
Eine Begründung der hyperbolischen Geometrie (1954) (13)
Beweis des Desarguesschen Satzes aus der Reidemeisterfigur und verwandte Sätze (1955) (13)
Proof of the Caratheodory Conjecture by Mean Curvature Flow in the Space of Oriented Affine Lines (2008) (13)
Flächentheorie im Großen (1973) (13)
Neue Ergebnisse über konvexe Flächen (1960) (12)
Real hypersurfaces of Kahler manifolds. (2001) (11)
The space of closed curves on the sphere (1968) (11)
Simple closed geodesics on pinched spheres (1968) (10)
On the space of oriented affine lines in $$ \mathbb{R}^3 $$ (2004) (10)
The theorem of the three closed geodesics (1965) (10)
PARABOLIC CLASSICAL CURVATURE FLOWS (2015) (9)
A neutral Kähler surface with applications in geometric optics (2008) (9)
PROJEKTIVE GEOMETRIE UND LINEARE ALGEBRA ÜBER VERALLGEMEINERTEN BEWERTUNGSRINGEN (1962) (9)
On the Space of Oriented Affine Lines in $R^3$ (2004) (9)
Der indexsatz für geschlossene Geodätische (1974) (9)
Remarks on the injectivity radius estimate for almost 1/4-pinched manifolds (1986) (8)
Asymptotic curves on real analytic surfaces inC2 (1985) (8)
Eine Kennzeichnung der Riemannschen sowie der Hermiteschen Mannigfaltigkeiten (1958) (8)
Über das Einspannungsproblem in der projektiven und affinen Differentialgeometrie (1952) (7)
A Neutral Kaehler Metric on Space of Time-like Lines in Lorentzian 3-space (2006) (7)
On area-stationary surfaces in certain neutral Kaehler 4-manifolds (2006) (7)
On Weingarten surfaces in Euclidean and Lorentzian 3-space (2010) (7)
Closed geodesics on surfaces of genus 0 (1979) (7)
On the number of closed geodesics on a riemannian manifold (1964) (7)
Orthogonal groups over local rings (1961) (6)
Totally null surfaces in neutral Kähler 4-manifolds. (2008) (6)
THE SPACE OF CLOSED CURVES ON A PROJECTIVE SPACE (1969) (5)
Evolving to non-round Weingarten spheres: integer linear Hopf flows (2017) (5)
2.2 Symmetric Spaces (1995) (5)
Reflection of a wave off a surface (2004) (5)
A Global Version of a Classical Result of Joachimsthal (2014) (5)
On $\mathrm{C}^2$-smooth Surfaces of Constant Width (2007) (5)
On C$^2$-smooth Surfaces of Constant Width (2007) (4)
Level Sets of Functions and Symmetry Sets of Surface Sections (2005) (4)
THE INDEX THEOREM FOR CLOSED GEODESICS (1974) (4)
From Global to Local: an index bound for umbilic points on smooth convex surfaces (2012) (4)
Über die 2-dimensionalen Flächen im 4-dimensionalen projektiven Raum (1952) (4)
On the topology of Riemannian manifolds where the conjugate points have a similar distribution as in symmetric spaces of rank 1 (1963) (4)
The Geodesic Flow (1978) (4)
Über kompakte Riemannsche Mannigfaltigkeiten (1959) (4)
Über die Arfsche Invariante quadratischer Formen mod 2. (1954) (4)
The Casimir Effect Between Non-Parallel Plates by Geometric Optics (2004) (3)
Existence of infinitely many closed geodesics (1976) (3)
Area-stationary surfaces in neutral Kähler 4-manifolds. (2008) (3)
3.8 Manifolds of Non-Positive Curvature (1995) (3)
Mean curvature flow of compact spacelike submanifolds in higher codimension (2018) (3)
Generalised Surfaces in ${\Bbb{R}}^3$ (2004) (3)
Reflection in a Translation Invariant Surface (2005) (3)
Lineare Gruppen über verallgemeinerten Bewertungsringen (1961) (2)
A pr 2 00 5 Level sets of functions and symmetry sets of smooth surface sections (2005) (2)
Grassmannian Manifolds in Geometry (1996) (2)
Intrinsic Geometry of Surfaces: Local Theory (1978) (2)
Über die Arfsche Invariante quadratischer Formen mod 2 (1991) (2)
A Converging Lagrangian Curvature Flow in the Space of Oriented Lines (2013) (2)
Real Surfaces in Complex Surfaces (2001) (2)
Hyperbolic Closed Geodesics (1973) (2)
A CONVERGING LAGRANGIAN FLOW IN THE SPACE OF ORIENTED LINES (2016) (2)
Mathematik und Melancholie : von Albrecht Dürer bis Robert Musil (1997) (2)
The Global Geometry of Surfaces (1978) (2)
ON THE STRUCTURE OF COMPACT RIEMANNIAN MANIFOLDS. (1958) (2)
Prescribed k-symmetric curvature hypersurfaces in de Sitter space (2019) (1)
Zur Riemannschen Geometrie auf Hilbertmannigfaltigkeiten (1972) (1)
Die Bedeutung von Christoffel für die Geometrie (1981) (1)
Affine Ebenen mit Orthogonalität (1957) (1)
Closed curves on S2 with bounded winding number (1983) (1)
Geodesic Flow on Global Holomorphic Sections of ${TS}^2$ (2006) (1)
Book Review: Affine differential geometry (1996) (1)
Über den Index geschlossener Geodätischer auf Flächen (1978) (1)
The Existence of Three Short Closed Geodesics (1985) (1)
Stability of the Bishop familyοf holomorphic discs (1997) (1)
On compact Kaehlerian manifolds with positive holomorphic curvature. (1961) (1)
Geodesic Flow on the Normal Congruence of a Minimal Surface (2006) (1)
Fredholm-Regularity of Holomorphic Discs in Plane Bundles over Compact Surfaces (2018) (1)
Poincaré’s closed geodesic on a convex surface (2004) (1)
2.6 Appendix – The Injectivity Radius for 1/4-pinched Manifolds (1995) (1)
Erratum to: On the geometry of spaces of oriented geodesics (2016) (1)
Fredholm-regularity of holomorphic disks in plane bundles. (2018) (1)
On the Existence of Many Closed Geodesics (1978) (1)
Sphärische Kurven mit beschränkter Selbstschnittzahl (1982) (1)
3.4 Geodesics on Surfaces (1995) (0)
1.9 Geodesics and Convex Neighborhoods (1995) (0)
The Hilbert Manifold of Closed Curves (1978) (0)
2.7 Comparison Theorems for Triangles (1995) (0)
Asymptotics in a Riemann-Hilbert boundary problem for pseudoholomorphic curves (2001) (0)
2.5 The Second Order Neighborhood of a Critical Point (1983) (0)
1.8 Riemannian Manifolds (1995) (0)
The Geometry of Focal Sets (2004) (0)
3.10 The Main Theorem for Surfaces of Genus 0 (1995) (0)
Surfaces: local theory (1978) (0)
On a proof of divisibility lemma, I (1985) (0)
Two-Dimensional Riemannian Geometry (1978) (0)
Erratum to the review of “Affine differential geometry” (1999) (0)
1.11 Riemannian Curvature (1995) (0)
1.12 Jacobi Fields (1995) (0)
2.1 Completeness and Cut Locus (1995) (0)
3.2 Properties of the Geodesic Flow (1995) (0)
2.8 The Sphere Theorem (1995) (0)
2.1 Appendix – Orientation (1995) (0)
Calculus in Euclidean Space (1978) (0)
3.6 Closed Geodesies on Spheres (1995) (0)
2.6 Index and Curvature (1995) (0)
3.3 Stable and Unstable Motions (1995) (0)
3.1 Hamiltonian Systems (1995) (0)
2.4 The Loop Space and the Space of Closed Curves (1983) (0)
The triangle theorem in the Riemannian geometry (1964) (0)
Closed geodesics on spheres (1983) (0)
2022 CONJUGATE POINTS IN SUB-RIEMANNIAN GEOMETRY (0)
2.3 The Hilbert Manifold of H1-curves (1995) (0)
2.9 Non-compact Manifolds of Positive Curvature (1995) (0)
Stable and unstable motions on surfaces (1980) (0)
2.5 Appendix – The S1- and the Ζ2-action on AM (1995) (0)
1.0 Review of Differential Calculus and Topology (1995) (0)
1.1 Differentiable Manifolds (1995) (0)
Erratum to: On the geometry of spaces of oriented geodesics (2016) (0)
On Hamilton's Characteristic Functions for Reflection (2006) (0)
1.4 Vector Fields and Tensor Fields (1995) (0)
3.5 Geodesics on the Ellipsoid (1995) (0)
1.6 The Exponential Mapping (1995) (0)
1.10 Isometric Immersions (1995) (0)
The Hilbert manifold of ¹-curves (1983) (0)
The Theory of Closed Geodesics (2009) (0)
GENERALISED SURFACES IN ℝ³ (2004) (0)
1.2 Tensor Bundles (1995) (0)
1.7 Lie Groups (1995) (0)
Selected papers of Wilhelm P.A. Klingenberg (1991) (0)
1.3 Immersions and Submersions (1995) (0)
1.5 Covariant Derivation (1995) (0)
Symmetries of the Coffeecup Caustic (2004) (0)
On the existence of closed geodesics on spherical manifolds (1981) (0)
3.9 The Geodesic Flow on Manifolds of Negative Curvature (1995) (0)
The Morse-Lusternik-Schnirelmann Theory on the Manifold of Closed Curves (1978) (0)
Appendix. The ¹- and the ℤ₂-action on (1983) (0)
Plane Curves: Global Theory (1978) (0)
Über die Existenz unendlich vieler geschlossener Geodätischer (1991) (0)
Geschlossene Geodätische (1973) (0)
Beziehungen zwischen Krümmung und topologischer Gestalt (1975) (0)
Zur affinen Differentialgeometrie (1951) (0)
Baustoffe und ihr Gütenachweis (1950) (0)
Eigenwerte und Normalformen (1990) (0)
Vorläufige Richtlinien für die Bemessung von Verbundträgern im Straßenbrückenbau (1950) (0)
Riemannsche Mannigfaltigkeiten als metrische Räume (1968) (0)
2-dimensionale riemannsche Geometrie (1973) (0)
Hinweise für die Bemessung einzelner Bauteile (1950) (0)
Grundsätze für die bauliche Durchbildung (1950) (0)
Periodische Geodätische auf Kompakten Riemannschen Mannigfaltigkeiten (1972) (0)
Die Anzahl der Nullstellen eines Polynoms in Gebieten mit stückweise rationalen Randkurven (1956) (0)
Innere Flächentheorie: Lokale Theorie (1973) (0)
Extremaleigenschaften von Geodätischen (1975) (0)
Lineare Gleichungen und Determinanten (1992) (0)
Riemannigfaltigkeiten als metrische Räume (1975) (0)
Christoffel und die Differentialgeometrie (1981) (0)
Begriffsfestlegung und Geltungsbereich (1950) (0)
Die Riemannsche Mannigfaltigkeit H 1 (I,M) (1972) (0)
Kurven — Allgemeine Theorie (1973) (0)
Ebene Kurven im Großen (1973) (0)
Eine Charakterisierung von affinen Ebenen mit Orthogonalität (1958) (0)
Differenzierbare Mannigfaltigkeiten und Abbildungen (1968) (0)
Differentialrechnung im euklidischen Raum (1973) (0)
Nachweis der Bruchsicherheit (1950) (0)

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