Introduction to Riemannian manifolds
Author(s)
Bibliographic Information
Introduction to Riemannian manifolds
（Graduate texts in mathematics, 176）
Springer, c2018
2nd ed
- : [pbk]
- Other Title
-
Riemannian manifolds : an introduction to curvature
Related Bibliography 1 items
Available at / 3 libraries
-
No Libraries matched.
- Remove all filters.
Note
"Originally published with title "Riemannian manifolds : an introduction to curvature""--T.p. verso
Includes bibliographical references (p. 415-418) and indexes
Description and Table of Contents
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.
by "Nielsen BookData"
