大葉大學圖書館 |

Riemannian geometry[electronic resource] /

紀錄類型:	書目-語言資料,印刷品 : Monograph/item
杜威分類號:	516.373
書名/作者:	Riemannian geometry/ by Peter Petersen.
作者:	Petersen, Peter.
出版者:	Cham : : Springer International Publishing :, 2016.
面頁冊數:	xviii, 499 p. : : ill., digital ;; 24 cm.
Contained By:	Springer eBooks
標題:	Geometry, Riemannian.
標題:	Mathematics.
標題:	Differential Geometry.
ISBN:	9783319266541
ISBN:	9783319266527
內容註:	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.
摘要、提要註:	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.
電子資源:	http://dx.doi.org/10.1007/978-3-319-26654-1

Riemannian geometry[electronic resource] /
Petersen, Peter.

Riemannian geometry[electronic resource] /by Peter Petersen. - 3rd ed. - Cham :Springer International Publishing :2016. - xviii, 499 p. :ill., digital ;24 cm. - Graduate texts in mathematics,1710072-5285 ;. - Graduate texts in mathematics ;263..

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.

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.

ISBN: 9783319266541

Standard No.: 10.1007/978-3-319-26654-1doiSubjects--Topical Terms:

511012
Geometry, Riemannian.

LC Class. No.: QA649

Dewey Class. No.: 516.373

Riemannian geometry[electronic resource] /
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