The Chern Symposium 1979

1. Front Matter

   Pages i-vii

   PDF

2. Real and Complex Geometry in Four Dimensions

   • M. F. Atiyah

   Pages 1-10

3. Equivariant Morse Theory and the Yang-Mills Equation on Riemann Surfaces

   • Raoul Bott

   Pages 11-22

4. Isometric Families of Kähler Structures

   • Eugenio Calabi

   Pages 23-39

5. Two Applications of Algebraic Geometry to Entire Holomorphic Mappings

   • Mark Green, Phillip Griffiths

   Pages 41-74

6. The Canonical Map for Certain Hilbert Modular Surfaces

   • F. Hirzebruch

   Pages 75-95

7. Tight Embeddings and Maps. Submanifolds of Geometrical Class Three in E ^N

   • Nicolaas H. Kuiper

   Pages 97-145

8. Geometry of Quadrics and Spectral Theory

   • J. Moser

   Pages 147-188

9. Remarks on Nonlinear Problems

   • Louis Nirenberg

   Pages 189-197

10. Minimal Surfaces, Gauss Maps, Total Curvature, Eigenvalue Estimates, and Stability

    • Robert Osserman

    Pages 199-227

11. de Rham-Sullivan Measure of Spaces and Its Calculability

    • Wu Wen-tsün

    Pages 229-245

12. Fibre Bundles and the Physics of the Magnetic Monopole

    • Chen Ning Yang

    Pages 247-253

13. The Total Mass and the Topology of an Asymptotically Flat Space-Time

    • Shing-Tung Yau

    Pages 255-259

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 .

• Differentialgeometrie
• Minimal surface
• curvature
• differential geometry
• manifold

• Department of Mathematics, University of California, Berkeley, USA

  W.-Y. Hsiang, S. Kobayashi, I. M. Singer, J. Wolf, H.-H. Wu

• Department of Mathematics, California Institute of Technology, Pasadena, USA

  A. Weinstein

Policies and ethics