Riemannian submersions from compact four manifolds

Xiaoyang Chen

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arXiv · 1409.4027

Riemannian submersions from compact four manifolds

Xiaoyang Chen

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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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Xiaoyang Chen. 2014-09-14. Riemannian submersions from compact four manifolds. https://arxiv.org/abs/1409.4027

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