Selected Papers II

ISBN-13: 9781461489764 / Angielski / Miękka / 2013 / 444 str.

Shiing-Shen Chern

Opis

In recognition of professor Shiing-Shen Chern's long and distinguished service to mathematics and to the University of California, the geometers at Berkeley held an International Symposium in Global Analysis and Global Geometry in his honor in June 1979. The output of this Symposium was published in a series of three separate volumes, comprising approximately a third of Professor Chern's total publications up to 1979. Later, a fourth volume was published, focusing on papers written during the Eighties. This second volume comprises selected papers written between 1932 and 1965.

Spis treści

[1] Pairs of Plane Curves with Points in One-to-One Correspondence.- [3] Associate Quadratic Complexes of a Rectilinear Congruence.- [6] Sur la Géométrie d’une Équation Différentielle du Troisième Ordre.- [8] On Projective Normal Coordinates.- [9] On Two Affine Connections.- [10] Sur la Géométrie d’un Système d’Équations Différentielles du Second Ordre.- [12] Sur les Invariants Intégraux en Géométrie.- [14] Sur une Généralisation d’une Formule de Crofton.- [15] Sulla Formula Principale Cinematica dello Spazio ad n dimensioni (with Chih-ta Yen).- [17] Sur les Invariants de Contact en Géométrie Projective Différentielle.- [20] The Geometry of Isotropic Surfaces.- [21] On a Weyl Geometry Defined from an (n - 1) Parameter Family of Hypersurfaces in a Space of n Dimensions.- [22] On the Euclidean Connections in a Finsler Space.- [24] Laplace Transforms of a Class of Higher Dimensional Varieties in a Projective Space of n Dimensions.- [26] Integral Formulas for the Characteristic Classes of Sphere Bundles.- [29] Some New Characterizations of the Euclidean Sphere.- [32] Some New Viewpoints in Differential Geometry in the Large.- [34] Differential Geometry in Symplectic Space I (with Hsien-chung Wang).- [40] Note on Projective Differential Line Geometry.- [42] Local Equivalence and Euclidean Connections in Finsler Spaces.- [43] The Imbedding Theorem for Fibre Bundles (with Yi-Fone Sun).- [45] The Homology Structure of Sphere Bundles (with E. Spanier).- [46] Differential Geometry of Fiber Bundles.- [48] On the Kinematic Formula in the Euclidean Space of n Dimensions.- [49] Élie Cartan and his Mathematical Work (with Claude Chevalley).- [50] Some Theorems on the Isometric Imbedding of Compact Riemann Manifolds in Euclidean Space (with Nicolaas H. Kuiper).- [53] Relations Between Riemannian and Hermitian Geometries.- [56] La Géométrie des Sous-Variétés d’un Espace Euclidien a Plusieurs Dimensions.- [57] An Elementary Proof of the Existence of Isothermal Parameters on a Surface.- [58] On Special W-Surfaces.- [59] On Curvature and Characteristic Classes of a Riemann Manifold.- [64] A Proof of the Uniqueness of Minkowski’s Problem for Convex Surfaces.- [66] On the Total Curvature of Immersed Manifolds, II (with Richard K. Lashof).- [67] Differential Geometry and Integral Geometry.- [77] On the Isometry of Compact Submanifolds in Euclidean Space (with Chuan-chih Hsiung).- [80] Hermitian Vector Bundles and the Equidistribution of the Zeroes of their Holomorphic Sections (with Raoul Bott).- List of Ph.D Theses Written Under the Supervision of S.S. Chern.- Permissions.

O autorze

Shiing-Shen Chern (October 26, 1911 – December 3, 2004) was a Chinese-born American mathematician and is regarded as one of the leaders in differential geometry of the twentieth century. Chern graduated from Nankai University in Tianjin, China in 1930; he received an M.S. degree in 1934 from Tsinghua University in Beijing and his doctorate from the University of Hamburg, Germany in 1936. A year later he returned to Tsinghua as a Professor of Mathematics. Chern was a member of the Institute for Advanced Study at Princeton, New Jersey, from 1943 to 1945. In 1946 he returned to China to become Acting Director of the Institute of Mathematics at the Academia Sinica in Nanjing. Chern returned to the United States in 1949 and taught at the University of Chicago, where he collaborated with André Weil, and later at the University of California in Berkeley. In 1961 he became a naturalized U.S. citizen. Chern served as Vice-President of the American Mathematical Society (1963–64) and was elected to both the National Academy of Sciences and the American Academy of Arts and Sciences. He was awarded the National Medal of Science in 1975 and the Wolf Prize in 1983. He helped found and was the director of the Mathematical Sciences Research Institute in Berkeley (1981–84) and in 1985 played an important role in the establishment of the Nankai Institute of Mathematics in Tianjin, where he held several posts, including director, until his death.