, Volume 64, Issue 2, pp 213-226

∑-flat manifolds and Riemannian submersions

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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.

Research supported by the Heinrich Hertz Foundation (first author), and by grant DMS88-01999 from the National Science Foundation (second author).