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An Introduction to Isometric Group Actions with Applications to Spaces with Curvature Bounded from Below

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Geometry of Manifolds with Non-negative Sectional Curvature

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 2110))

Abstract

We present a three part survey of previous and recent results in the theory of isometric group actions with applications to spaces with curvature bounded below. The first part consists of a review of basic material on isometric group actions. The second part covers the classical theorem of Hsiang and Kleiner about positively curved four manifolds admitting an isometric circle action. The third section covers recent joint work of the author with Galaz-García on the structure of cohomogeneity one Alexandrov spaces.

2000 Mathematics Subject Classification. Primary: 53C20; Secondary: 57S25, 51M25

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Notes

  1. 1.

    The author was supported in part by CONACYT Project #SEP-106923.

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Authors and Affiliations

  1. Department of Mathematics, Oregon State University, 368 Kidder Hall, Corvallis, OR, 97331, USA

    Catherine Searle

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  1. Catherine Searle
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Correspondence to Catherine Searle .

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Searle, C. (2014). An Introduction to Isometric Group Actions with Applications to Spaces with Curvature Bounded from Below. In: Geometry of Manifolds with Non-negative Sectional Curvature. Lecture Notes in Mathematics, vol 2110. Springer, Cham. https://doi.org/10.1007/978-3-319-06373-7_2

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