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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Research supported by the Heinrich Hertz Foundation (first author), and by grant DMS88-01999 from the National Science Foundation (second author).
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Strake, M., Walschap, G. ∑-flat manifolds and Riemannian submersions. Manuscripta Math 64, 213–226 (1989). https://doi.org/10.1007/BF01160120
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DOI: https://doi.org/10.1007/BF01160120