Riemannian manifolds and homogeneous geodesics
著者
書誌事項
Riemannian manifolds and homogeneous geodesics
（Springer monographs in mathematics）
Springer, c2020
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注記
Includes bibliographical references (p. 453-472) and indexes
内容説明・目次
内容説明
This book is devoted to Killing vector fields and the one-parameter isometry groups of Riemannian manifolds generated by them. It also provides a detailed introduction to homogeneous geodesics, that is, geodesics that are integral curves of Killing vector fields, presenting both classical and modern results, some very recent, many of which are due to the authors. The main focus is on the class of Riemannian manifolds with homogeneous geodesics and on some of its important subclasses.
To keep the exposition self-contained the book also includes useful general results not only on geodesic orbit manifolds, but also on smooth and Riemannian manifolds, Lie groups and Lie algebras, homogeneous Riemannian manifolds, and compact homogeneous Riemannian spaces.
The intended audience is graduate students and researchers whose work involves differential geometry and transformation groups.
目次
Introduction. - 1 Riemannian Manifolds. - 2 Lie Groups and Lie Algebras. - 3 Isometric Flows and Killing Vector Fields on Riemannian Manifolds. - 4 Homogeneous Riemannian Manifolds. - 5 Manifolds With Homogeneous Geodesics. - 6 Generalized Normal Homogeneous ManifoldsWith Intrinsic Metrics. - 7 Clifford-Wolf Homogeneous Riemannian Manifolds. - References. - List of Tables. - Index.
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