Katsumi Nomizu

NomizuNomizu, Katsumi
Katsumi Nomizu was a Japanese-American mathematician known for his work in differential geometry.wikipedia
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Foundations of Differential Geometry

During this time he embarked on a major collaborative project with Professor Shoshichi Kobayashi at the University of California, Berkeley, resulting in the classic two-volume work, Foundations of Differential Geometry in 1963.
Foundations of Differential Geometry is an influential 2-volume mathematics book on differential geometry written by Shoshichi Kobayashi and Katsumi Nomizu.

Shiing-Shen Chern

S. S. ChernChernChen Xingshen
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.
Two of his students Manfredo do Carmo and Katsumi Nomizu have written influential textbooks in geometry.

Shoshichi Kobayashi

KobayashiKobayashi, Shoshichi
During this time he embarked on a major collaborative project with Professor Shoshichi Kobayashi at the University of California, Berkeley, resulting in the classic two-volume work, Foundations of Differential Geometry in 1963.
The two-volume book Foundations of differential geometry (1963-1969), which he coauthored with Katsumi Nomizu, has been known for its wide influence.

Kulkarni–Nomizu product

Kulkarni-Nomizu product
In the mathematical field of differential geometry, the Kulkarni–Nomizu product (named for Ravindra Shripad Kulkarni and Katsumi Nomizu) is defined for two (0,2)-tensors and gives as a result a (0,4)-tensor.

Mathematician

mathematiciansapplied mathematicianMathematics
Katsumi Nomizu was a Japanese-American mathematician known for his work in differential geometry.

Differential geometry

differentialdifferential geometerdifferential geometry and topology
Katsumi Nomizu was a Japanese-American mathematician known for his work in differential geometry.

Osaka

Osaka, JapanŌsakaOsaka, Osaka
Nomizu was born in Osaka, Japan on the first day of December, 1924.

Mathematics

mathematicalmathmathematician
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.

Osaka University

University of OsakaOsaka Imperial UniversityOsaka
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.

Master of Science

M.S.MScMS
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.

Nagoya University

University of NagoyaNagoyaNagoya Imperial University
Returning to Japan, he studied at Nagoya University, obtaining a doctor of science in 1955.

Doctor of Science

DScD.Sc.Sc.D.
Returning to Japan, he studied at Nagoya University, obtaining a doctor of science in 1955.

Brown University

BrownCollege in the English Colony of Rhode Island and Providence PlantationsBrown Association for Cooperative Housing
In 1960 he began his thirty-five-year career with Brown University, first as associate professor, then becoming full professor in 1963.

Associate professor

Associateassociate professorsAssoc. Prof.
In 1960 he began his thirty-five-year career with Brown University, first as associate professor, then becoming full professor in 1963.

Doctor of Philosophy

Ph.D.PhDPh.D
In his teaching career he helped 13 students from Brown and 1 from MIT obtain a Ph.D. According to the Mathematics Genealogy Project, Professor Nomizu has seventeen mathematical grandchildren.

American Mathematical Society

AMSChelsea PublishingNew York Mathematical Society
He served as editor of a collection of papers on number theory and algebraic geometry published by the American Mathematical Society in 1996.

Providence, Rhode Island

ProvidenceProvidence, RIProvidence, R.I.
Professor Nomizu died on November 5, 2008, in Providence, Rhode Island.

Humboldt Prize

Humboldt Research AwardAlexander von Humboldt Research AwardAlexander von Humboldt Award

Ernst Ruh

Ernst Alfred RuhRuh, Ernst
Ernst Ruh received his doctorate in 1964 from Brown University under Katsumi Nomizu with thesis On the Automorphism Groups of a G-structure.

Riemannian connection on a surface

Cartan's first and second structure equationscovariant surface derivativesuccinctly expressed and derived
Cartan's approach was rephrased in the modern language of principal bundles by Ehresmann, after which the subject rapidly took its current form following contributions by Chern, Ambrose and Singer, Kobayashi, Nomizu, Lichnerowicz and others.

Affine geometry

affineaffine ''d''-spaceaffine geometries
In 1984, "the affine plane associated to the Lorentzian vector space L 2 " was described by Graciela Birman and Katsumi Nomizu in an article entitled "Trigonometry in Lorentzian geometry".

Symmetric space

Riemannian symmetric spacesymmetric spaceslocally symmetric space
As shown by Katsumi Nomizu, there is a dichotomy: an irreducible symmetric space G/H is either flat (i.e., an affine space) or \mathfrak g is semisimple.

Curvature form

Bianchi identityBianchi identitiescurvature
* Shoshichi Kobayashi and Katsumi Nomizu (1963) Foundations of Differential Geometry, Vol.I, Chapter 2.5 Curvature form and structure equation, p 75, Wiley Interscience.