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arXiv · 1703.09240

Random Manifolds have no Totally Geodesic Submanifolds

Thomas Murphy·Frederick Wilhelm
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Abstract

For $n\geq 4$ we show that generic closed Riemannian $n$-manifolds have no nontrivial totally geodesic submanifolds, answering a question of Spivak. An immediate consequence is a severe restriction on the isometry group of a generic Riemannian metric. Both results are widely believed to be true, but we are not aware of any proofs in the literature.

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Thomas Murphy, Frederick Wilhelm. 2017-03-27. Random Manifolds have no Totally Geodesic Submanifolds. https://arxiv.org/abs/1703.09240

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