Riemannian geometry

著者

• Petersen, Peter

書誌事項

Riemannian geometry

Peter Petersen

（Graduate texts in mathematics, 171）

Springer, c2006

2nd ed

注記

Bibliography: p. 393-396

Includes index

内容説明・目次

内容説明

This volume introduces techniques and theorems of Riemannian geometry, and opens the way to advanced topics. The text combines the geometric parts of Riemannian geometry with analytic aspects of the theory, and reviews recent research. The updated second edition includes a new coordinate-free formula that is easily remembered (the Koszul formula in disguise); an expanded number of coordinate calculations of connection and curvature; general fomulas for curvature on Lie Groups and submersions; variational calculus integrated into the text, allowing for an early treatment of the Sphere theorem using a forgotten proof by Berger; recent results regarding manifolds with positive curvature.

目次

Riemannian Metrics.- Curvature.- Examples.- Hypersurfaces.- Geodesics and Distance.- Sectional Curvature Comparison I.- The Bochner Technique.- Symmetric Spaces and Holonomy.- Ricci Curvature Comparison.- Convergence.- Sectional Curvature Comparison II.

「Nielsen BookData」 より

• NII書誌ID(NCID): BA7834115X
• ISBN:
  • 0387292462
• LCCN: 2006923825
• 出版国コード: us
• タイトル言語コード: eng
• 本文言語コード: eng
• 出版地: New York
• ページ数/冊数: xv, 401 p.
• 大きさ: 24 cm
• 件名:
  • LCSH : Geometry, Riemannian
• 親書誌ID:
  • BA00010074