リーマン多様体入門（テキスト・第２版） Introduction to Riemannian Manifolds〈2nd ed. 2018〉（2）

著者名：Lee, John M.

Springer（2019/01/02発売）

• 言語：ENG
• ISBN：9783319917542
• eISBN：9783319917559

Description

This text focuses on developing an intimate acquaintance with the geometric meaning of curvature and thereby introduces and demonstrates all the main technical tools needed for a more advanced course on Riemannian manifolds. It covers proving the four most fundamental theorems relating curvature and topology: the Gauss-Bonnet Theorem, the Cartan-Hadamard Theorem, Bonnet’s Theorem, and a special case of the Cartan-Ambrose-Hicks Theorem.

Table of Contents

Preface.- 1. What Is Curvature?.- 2. Riemannian Metrics.- 3. Model Riemannian Manifolds.- 4. Connections.- 5. The Levi-Cevita Connection.- 6. Geodesics and Distance.- 7. Curvature.- 8. Riemannian Submanifolds.- 9. The Gauss–Bonnet Theorem.- 10. Jacobi Fields.- 11. Comparison Theory.- 12. Curvature and Topology.- Appendix A: Review of Smooth Manifolds.- Appendix B:  Review of Tensors.- Appendix C: Review of Lie Groups.- References.- Notation Index.- Subject Index.