The Chern Symposium 1979: Proceedings of the International Symposium on Differential Geometry in honor of S.-S. Chern, held in Berkeley, California, June 1979

Description

This volume attests to the vitality of differential geometry as it probes deeper into its internal structure and explores ever widening connections with other subjects in mathematics and physics. To most of us Professor S. S. Chern is modern differential geometry, and we, his students, are grateful to him for leading us to this fertile landscape. The aims of the symposium were to review recent developments in geometry and to expose and explore new areas of research. It was our way of honoring Professor Chern upon the occasion of his official retirement as Professor of Mathematics at the University of California. This book is a record of the scientific events of the symposium and reflects Professor Chern's wide interest and influence. The conference also reflected Professor Chern's personality. It was a serious occasion, active yet relaxed, mixed with gentleness and good humor. We wish him good health, a long life, happiness, and a continuation of his extraordinarily deep and original contributions to mathematics. I. M. Singer Contents Real and Complex Geometry in Four Dimensions M. F. ATIYAH. . . . . . . . . . . . . Equivariant Morse Theory and the Yang-Mills Equation on Riemann Surfaces RAOUL BaTT .. 11 Isometric Families of Kahler Structures EUGENIO CALABI. . 23 Two Applications of Algebraic Geometry to Entire Holomorphic Mappings MARK GREEN AND PHILLIP GRIFFITHS. • . . . • . . 41 The Canonical Map for Certain Hilbert Modular Surfaces F. HIRZEBRUCH . . . . . • . . . . . . . . . 75 Tight Embeddings and Maps. Submanifolds of Geometrical Class Three in EN NICOLAAS H. KUIPER . Front Matter....Pages i-vii Real and Complex Geometry in Four Dimensions....Pages 1-10 Equivariant Morse Theory and the Yang-Mills Equation on Riemann Surfaces....Pages 11-22 Isometric Families of Kähler Structures....Pages 23-39 Two Applications of Algebraic Geometry to Entire Holomorphic Mappings....Pages 41-74 The Canonical Map for Certain Hilbert Modular Surfaces....Pages 75-95 Tight Embeddings and Maps. Submanifolds of Geometrical Class Three in E N ....Pages 97-145 Geometry of Quadrics and Spectral Theory....Pages 147-188 Remarks on Nonlinear Problems....Pages 189-197 Minimal Surfaces, Gauss Maps, Total Curvature, Eigenvalue Estimates, and Stability....Pages 199-227 de Rham-Sullivan Measure of Spaces and Its Calculability....Pages 229-245 Fibre Bundles and the Physics of the Magnetic Monopole....Pages 247-253 The Total Mass and the Topology of an Asymptotically Flat Space-Time....Pages 255-259