Riemannian geometry
著者
書誌事項
Riemannian geometry
（Graduate texts in mathematics, 171）
Springer, c2016
3rd ed
- : pbk
大学図書館所蔵 件 / 全47件
-
該当する所蔵館はありません
- すべての絞り込み条件を解除する
注記
Bibliography: p. 491-494
Includes index
内容説明・目次
内容説明
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.
From reviews of the first edition:
"The book can be highly recommended to all mathematicians who want to get a more profound idea about the most interesting achievements in Riemannian geometry. It is one of the few comprehensive sources of this type."
Bernd Wegner, ZbMATH
目次
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.
「Nielsen BookData」 より