A Mathematician and His Mathematical Work

by Chern, Shiing-Shen; Li, P.; Cheng, S. Y.; Tian, G.

• ISBN13: 9789810223854
• ISBN10: 9810223854
• Format: Hardcover
• Copyright: 1996-06-01
• Publisher: World Scientific Pub Co Inc

Table of Contents

Foreword
The Life and Mathematics of Shiing-Shen Chern	p. 1
My Mathematical Education	p. 46
A Summary of My Scientific Life and Works	p. 61
S. S. Chern as Geometer and Friend	p. 72
Some Reflections on the Mathematical Contributions of S. S. Chern	p. 76
Shiing-Shen Chern as Friend and Mathematician	p. 83
Abzahlungen fur Gewebe	p. 95
On Integral Geometry in Klein Spaces	p. 103
A Simple Intrinsic Proof of the Gauss-Bonnet Formula for Closed Riemannian Manifolds	p. 115
On the Curvatura Integra in a Riemannian Manifold	p. 121
Characteristic Classes of Hermitian Manifolds	p. 132
Sur une Classe Remarquable de Varietes dans l'espace Projectif a N Dimensions	p. 169
A Theorem on Orientable Surfaces in Four-Dimensional Space	p. 178
On the Kinematic Formula in the Euclidean Space of N Dimensions	p. 183
On a Generalization of Kahler Geometry	p. 193
On the Total Curvature of Immersed Manifolds	p. 212
On the Index of a Fibered Manifold	p. 225
On the Total Curvature of Immersed Manifolds, II	p. 235
Integral Formulas for Hypersurfaces in Euclidean Space and Their Applications to Uniqueness Theorems	p. 243
A Uniqueness Theorem on Closed Convex Hypersurfaces in Euclidean Space	p. 252
The Integrated Form of the First Main Theorem for Complex Analytic Mappings in Several Complex Variables	p. 256
Hermitian Vector Bundles and the Equidistribution of the Zeroes of Their Holomorphic Sections	p. 272
On the Kinematic Formula in Integral Geometry	p. 314
Intrinsic Norms on a Complex Manifold	p. 332
Some Formulas Related to Complex Transgression	p. 353
Characteristic Forms and Geometric Invariants	p. 363
Real Hypersurfaces in Complex Manifolds	p. 385
An Analogue of Backlund's Theorem in Affine Geometry	p. 438
From Triangles to Manifolds	p. 458
Lie Groups and KdV Equations	p. 469
Deformation of Surfaces Preserving Principal Curvatures	p. 480
Dupin Submanifolds in Lie Sphere Geometry	p. 491
Historical Remarks on Gauss-Bonnet	p. 539
What is Geometry?	p. 548
An Introduction to Dupin Submanifolds	p. 556
Families of Hypersurfaces under Contact Transformations in R[superscript n]	p. 564
Surface Theory with Darboux and Bianchi	p. 572
Transgression in Associated Bundles	p. 583
Characteristic Classes and Characteristic Forms	p. 594
On Finsler Geometry	p. 603
Yang-Mills Equations and Yang-Baxter Equations	p. 608
On a Notable Connection in Finsler Geometry	p. 613
Characteristic Classes as a Geometric Object	p. 659
Sophus Lie and Differential Geometry	p. 665
Projective Geometry and Riemann's Mapping Problem	p. 674
Curriculum Vitae	p. 695
List of Ph.D. Theses written under the supervision of S. S. Chern	p. 697
Bibliography of the Publications of S. S. Chern	p. 699
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