Geometriae Dedicata

, Volume 144, Issue 1, pp 101–114

A splitting theorem for infinite dimensional Alexandrov spaces with nonnegative curvature and its applications

Original Paper
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Abstract

We prove a splitting theorem for Alexandrov space of nonnegative curvature without properness assumption. As a corollary, we obtain a maximal radius theorem for Alexandrov spaces of curvature bounded from below by 1 without properness assumption. Also, we provide new examples of infinite dimensional Alexandrov spaces of nonnegative curvature.

Keywords

Alexandrov space Lower curvature bound Splitting theorem Maximal radius sphere theorem Infinite dimension 

Mathematics Subject Classification (2000)

53C20 53C21 

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Copyright information

© Springer Science+Business Media B.V. 2009

Authors and Affiliations

  1. 1.Graduate School of Pure and Applied SciencesUniversity of TsukubaTsukubaJapan

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