# Katsumi Nomizu

Japanese-American mathematician

## Katsumi Nomizu's AcademicInfluence.com Rankings

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Mathematics

## Katsumi Nomizu's Degrees

- PhD Mathematics University of Tokyo

## Why Is Katsumi Nomizu Influential?

(Suggest an Edit or Addition)According to Wikipedia, Katsumi Nomizu was a Japanese-American mathematician known for his work in differential geometry. Life and career Nomizu was born in Osaka, Japan on the first day of December, 1924. He studied mathematics at Osaka University, graduating in 1947 with a Master of Science then traveled to the United States on a U.S. Army Fulbright Scholarship. He studied first at Columbia University and then at the University of Chicago where in 1953 he became the first student to earn a Ph.D. under the thesis direction of Shiing-Shen Chern. The subject was affine differential geometry, a topic to which he would return much later in his career. He presented his thesis, Invariant affine connections on homogeneous spaces in 1953.

## Katsumi Nomizu's Published Works

### Published Works

- Foundations of Differential Geometry (1963) (5541)
- Foundations of Differential Geometry, Volume I. (1965) (596)
- Invariant Affine Connections on Homogeneous Spaces (1954) (520)
- On the Cohomology of Compact Homogeneous Spaces of Nilpotent Lie Groups (1954) (386)
- Affine Differential Geometry (1994) (353)
- The existence of complete Riemannian metrics (1961) (169)
- On Local and Global Existence of Killing Vector Fields (1960) (155)
- On circles and spheres in Riemannian geometry (1974) (154)
- Lie groups and differential geometry (1956) (152)
- A formula of Simons' type and hypersurfaces with constant mean curvature (1969) (142)
- ON HYPERSURFACES SATISFYING A CERTAIN CONDITION ON THE CURVATURE TENSOR (1968) (111)
- Trigonometry in Lorentzian Geometry (1984) (110)
- On the geometry of affine immersions (1987) (110)
- Left-invariant Lorentz metrics on Lie groups (1979) (85)
- Conjugate connections and Radon's theorem in affine differential geometry (1990) (83)
- Fundamentals of linear algebra (1966) (75)
- Some results in E. Cartan’s theory of isoparametric families of hypersurfaces (1973) (71)
- Differential geometry of complex hypersurfaces II (1968) (69)
- Characteristic roots and vectors of a diifferentiable family of symmetric matrices (1973) (64)
- Affine Differential Geometry: Geometry of Affine Immersions (2008) (63)
- Affine hypersurfaces with parallel cubic forms (1990) (60)
- Surfaces of revolution with constant mean curvature in Lorentz-Minkowski space (1984) (56)
- KINEMATICS AND DIFFERENTIAL GEOMETRY OF SUBMANIFOLDS (1978) (55)
- On sectional curvature of indefinite metrics. II (1978) (55)
- A NEW EQUIAFFINE THEORY FOR SURFACES IN ℝ4 (1993) (49)
- The axiom of spheres in Riemannian geometry (1971) (48)
- A new model of unimodular-affinely homogeneous surfaces (1991) (47)
- Cubic form Theorem for Affine Immersions (1988) (47)
- On the boundedness of Ricci curvature of an indefinite metric (1980) (45)
- Umbilical Submanifolds and Morse Functions (1972) (43)
- The Gauss-Bonnet theorem for $2$-dimensional spacetimes. (1984) (42)
- On isoparametric hypersurfaces in the Lorentzian space forms (1981) (40)
- Cayley surfaces in affine differential geometry (1989) (40)
- On isometric immersions of the hyperbolic plane into the Lorentz-Minkowski space and the Monge-Ampère equation of a certain type (1983) (38)
- On the gauss mapping for hypersurfaces of constant mean curvature in the sphere (1969) (36)
- On affine surfaces whose cubic forms are parallel relative to the affine metric (1989) (36)
- Centroaffine immersions of codimension two and projective hypersurface theory (1993) (34)
- A THEOREM ON CURVATURE TENSOR FIELDS. (1962) (33)
- Remarks on sectional curvature of an indefinite metric (1983) (31)
- On sectional curvature of indefinite metrics (1978) (31)
- A characterization of the Veronese varieties (1976) (27)
- On the group of affine transformations of an affinely connected manifold (1953) (27)
- On completeness in affine differential geometry (1986) (26)
- Conditions for constancy of the holomorphic sectional curvature (1973) (26)
- Studies on Riemannian Homogeneous Spaces (1955) (24)
- Isometric immersions of the hyperbolic plane into the hyperbolic space (1973) (21)
- On a certain class of homogeneous projectively flat manifolds (1987) (20)
- On Automorphisms of A Kählerian Structure (1957) (20)
- Recent development in the theory of connections and holonomy groups (1961) (20)
- ON FRENET EQUATIONS FOR CURVES OF CLASS C (1959) (17)
- Selected Papers on Harmonic Analysis, Groups, and Invariants (1997) (15)
- Isometric immersions of lorentzian space forms (1978) (15)
- UNIQUENESS OF THE NORMAL CONNECTIONS AND CONGRUENCE OF ISOMETRIC IMMERSIONS (1976) (15)
- Some results related to the equivalence problem in Riemannian geometry (1967) (14)
- On the geometry of affine Kähler immersions (1990) (13)
- On Flat Surfaces in S 1 3 and H 1 3 (1981) (13)
- On the rank and curvature of non-singular complex hypersurfaces in a complex projective space* (1969) (13)
- A Generalization of Lelieuvre’s Formula (1991) (12)
- Generalized central spheres and the notion of spheres in Riemannian geometry (1973) (12)
- On the geometry of projective immersions (1989) (12)
- On the spaces of generalized curvature tensor fields and second fundamental forms (1971) (11)
- Reduction Theorem for Connections and its Application to the Problem of Isotropy and Holonomy Groups of a Riemannian Manifold (1955) (11)
- The Lorentz-Poincar\'{e} metric on the upper half-space and its extension (1982) (9)
- On affine hypersurfaces with parallel nullity (1992) (9)
- On the Classification of Projectively Homogeneous Surfaces (1991) (9)
- GEODESICS IN AFFINE DIFFERENTIAL GEOMETRY (1995) (8)
- On normal and conormal maps for affine hypersurfaces (1992) (8)
- On the degree of differentiability of curves used in the definition of the holonomy group (1962) (6)
- On Infinitesimal Holonomy and Isotropy Groups (1957) (6)
- On infinitesimal transformations preserving the curvature tensor field and its covariant differentials (1964) (5)
- ON THE GROUP OF AUTOMORPHISMS OF A TOPOLOGICAI GROUP (1950) (4)
- Globally defined linear connections on the real line and the circle (1999) (3)
- On the convexity of spacelike hypersurfaces with nonpositive curvature (1983) (3)
- Another Rigidity Theorem for Affine Immersions (1995) (3)
- On the Cartan-Norden theorem for affine Kähler immersions (1991) (3)
- On certain quartic forms for affine surfaces (1992) (2)
- Lorentzian geometry for 2 × 2 real matrices (1991) (2)
- A characterization ofn-spheres in space forms and its complex analogue (1973) (1)
- Vector spaces and tensor algebras (1961) (1)
- Holonomy, Ricci tensor and Killing vector fields (1961) (1)
- Selected Papers on Analysis, Probability, and Statistics (1994) (0)
- Selected Papers on Number Theory and Algebraic Geometry (1996) (0)
- On a theorem of chern and terng on affine surfaces (1990) (0)
- HOLONOMY , RICCI TENSOR AND KILLING VECTOR FIELDS 1 (2010) (0)
- On Atine Surfaces whose Cubic Forms are Parallel Relative to the Ane Metric * (0)
- We Can Easily Check Lemma A.1. Matrices V and V Have the Property (0)
- Selected Papers on Analysis and Differential Equations (2003) (0)
- HOLONOMY, RICCI TENSOR AND KILLING (2010) (0)
- On the boundedness of Ricei curvature of an indef'mite metric (1980) (0)
- Selected Papers on Number Theory, Algebraic Geometry, and Differential Geometry (1994) (0)
- Selected Papers on Classical Analysis (2001) (0)

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