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Riemannian submersions from compact four manifolds

Authors
  • Chen, Xiaoyang1
  • 1 University of Notre Dame, Department of Mathematics, Notre Dame, IN, 46637, USA , Notre Dame (United States)
Type
Published Article
Journal
Mathematische Zeitschrift
Publisher
Springer Berlin Heidelberg
Publication Date
Sep 19, 2015
Volume
282
Issue
1-2
Pages
165–175
Identifiers
DOI: 10.1007/s00209-015-1536-2
Source
Springer Nature
Keywords
License
Yellow

Abstract

We show that under certain conditions, a nontrivial Riemannian submersion from positively curved four manifolds does not exist. This gives a partial answer to a conjecture due to Fred Wilhelm. We also prove a rigidity theorem for Riemannian submersions with totally geodesic fibers from compact four-dimensional Einstein manifolds.

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