manuscripta mathematica

, Volume 64, Issue 2, pp 213–226

∑-flat manifolds and Riemannian submersions

Authors

  • M. Strake
    • State University of New York
    • University of California
  • G. Walschap
    • State University of New York
    • University of California
Article

DOI: 10.1007/BF01160120

Cite this article as:
Strake, M. & Walschap, G. Manuscripta Math (1989) 64: 213. doi:10.1007/BF01160120

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.

Copyright information

© Springer-Verlag 1989