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manuscripta mathematica

, Volume 64, Issue 2, pp 213–226 | Cite as

∑-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.

Keywords

Maximal Volume Number Theory Algebraic Geometry Topological Group Distance Tube 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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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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