manuscripta mathematica

, Volume 64, Issue 2, pp 213–226

∑-flat manifolds and Riemannian submersions

  • M. Strake
  • G. Walschap
Article

Abstract

In this paper, we show that a certain rigidity condition (∑-flatness) for open nonnegatively curved manifoldsM is preserved by Riemannian submersions. The result can be applied to quotients ofM by groups of isometries. ∑-flat metrics are also used to derive a splitting theorem for distance tubes of maximal volume growth.

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Copyright information

© Springer-Verlag 1989

Authors and Affiliations

  • M. Strake
    • 1
    • 2
  • G. Walschap
    • 1
    • 2
  1. 1.State University of New YorkStony Brook
  2. 2.University of CaliforniaLos Angeles

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