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June 2019 Random Manifolds Have No Totally Geodesic Submanifolds
Thomas Murphy, Frederick Wilhelm
Michigan Math. J. 68(2): 323-335 (June 2019). DOI: 10.1307/mmj/1555034652

Abstract

For n4, we show that generic closed Riemannian n-manifolds have no nontrivial totally geodesic submanifolds, answering a question of Spivak. Although the result is widely believed to be true, we are not aware of any proof in the literature.

Citation

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Thomas Murphy. Frederick Wilhelm. "Random Manifolds Have No Totally Geodesic Submanifolds." Michigan Math. J. 68 (2) 323 - 335, June 2019. https://doi.org/10.1307/mmj/1555034652

Information

Received: 25 May 2017; Revised: 17 January 2018; Published: June 2019
First available in Project Euclid: 12 April 2019

zbMATH: 07084765
MathSciNet: MR3961219
Digital Object Identifier: 10.1307/mmj/1555034652

Subjects:
Primary: 53C20
Secondary: 53A99, 53C40

Rights: Copyright © 2019 The University of Michigan

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Vol.68 • No. 2 • June 2019
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