Introduction to Riemannian manifolds

書誌事項

Introduction to Riemannian manifolds

John M. Lee

(Graduate texts in mathematics, 176)

Springer, c2018

2nd ed

  • : [pbk]

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

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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詳細情報

  • NII書誌ID(NCID)
    BC11282638
  • ISBN
    • 9783030801069
  • LCCN
    2018943719
  • 出版国コード
    sz
  • タイトル言語コード
    eng
  • 本文言語コード
    eng
  • 出版地
    Cham
  • ページ数/冊数
    xiii, 437 p.
  • 大きさ
    25 cm
  • 親書誌ID
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