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

DOI: 10.1007/s10711-009-9390-1

Cite this article as:
Mitsuishi, A. Geom Dedicata (2010) 144: 101. doi:10.1007/s10711-009-9390-1

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 spaceLower curvature boundSplitting theoremMaximal radius sphere theoremInfinite dimension

Mathematics Subject Classification (2000)

53C2053C21

Copyright information

© Springer Science+Business Media B.V. 2009

Authors and Affiliations

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