Introduction to Riemannian manifolds
著者
書誌事項
Introduction to Riemannian manifolds
（Graduate texts in mathematics, 176）
Springer, 2021, c2018
2nd ed
- : softcover
- タイトル別名
-
Riemannian manifolds : an introduction to curvature
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注記
"Originally published with title "Riemannian manifolds : an introduction to curvature""--T.p. verso
"2nd ed.: (c) Springer International Publishing AG 2018. First softcover printing 2021"--T.p. verso
Includes bibliographical references (p. 415-418) and indexes
内容説明・目次
内容説明
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.
目次
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.
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