机读格式显示(MARC)
- 000 02997cam a2200361 i 4500
- 008 160210s2016 sz a b 001 0 eng d
- 020 __ |a 9783319266527 : |c CNY459.91
- 035 __ |a (OCoLC)938384433
- 040 __ |a YDXCP |b eng |c YDXCP |e rda |d NKM |d CFI |d OCLCF |d HCQ |d NHM |d AS |d MATH
- 050 _4 |a QA649 |b .P48 2016
- 050 _4 |a QA649 |b .P386 2016
- 100 1_ |a Petersen, Peter, |d 1962- |e author.
- 245 10 |a Riemannian geometry / |c Peter Petersen.
- 264 _1 |a Cham ; |a New York, NY : |b Springer International Publishing AG, |c c2016
- 300 __ |a xviii, 499 pages : |b illustrations ; |c 24 cm
- 336 __ |a text |b txt |2 rdacontent
- 337 __ |a unmediated |b n |2 rdamedia
- 338 __ |a volume |b nc |2 rdacarrier
- 490 1_ |a Graduate texts in mathematics ; |v 171.
- 504 __ |a Includes bibliographical references (pages 491-494) and index.
- 505 0_ |a Preface -- 1. Riemannian Metrics.-2. Derivatives -- 3. Curvature -- 4. Examples -- 5. Geodesics and Distance -- 6. Sectional Curvature Comparison I.- 7. Ricci Curvature Comparison.- 8. Killing Fields -- 9. The Bochner Technique -- 10. Symmetric Spaces and Holonomy -- 11. Convergence -- 12. Sectional Curvature Comparison II -- Bibliography -- Index.
- 505 0_ |a Riemannian Metrics -- Derivatives -- Curvature -- Examples -- Geodesics and Distance -- Sectional Curvature Comparison I -- Ricci Curvature Comparison -- Killing Fields -- The Bochner Technique -- Symmetric Spaces and Holonomy -- Convergence -- Sectional Curvature Comparison II.
- 520 __ |a "Intended for a one year course, this text serves as a single source, introducing readers to the important techniques and theorems, while also containing enough background on advanced topics to appeal to those students wishing to specialize in Riemannian geometry. This is one of the few Works to combine both the geometric parts of Riemannian geometry and the analytic aspects of the theory. The book will appeal to a readership that have a basic knowledge of standard manifold theory, including tensors, forms, and Lie groups. Important revisions to the third edition include: a substantial addition of unique and enriching exercises scattered throughout the text; inclusion of an increased number of coordinate calculations of connection and curvature; addition of general formulas for curvature on Lie Groups and submersions; integration of variational calculus into the text allowing for an early treatment of the Sphere theorem using a proof by Berger; incorporation of several recent results about manifolds with positive curvature; presentation of a new simplifying approach to the Bochner technique for tensors with application to bound topological quantities with general lower curvature bounds."--Back cover.
- 650 _0 |a Geometry, Riemannian.
- 830 _0 |a Graduate texts in mathematics.