The Michigan Mathematical Journal

Random Manifolds Have No Totally Geodesic Submanifolds

Thomas Murphy and Frederick Wilhelm

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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.

Article information

Source
Michigan Math. J., Volume 68, Issue 2 (2019), 323-335.

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

Permanent link to this document
https://projecteuclid.org/euclid.mmj/1555034652

Digital Object Identifier
doi:10.1307/mmj/1555034652

Mathematical Reviews number (MathSciNet)
MR3961219

Zentralblatt MATH identifier
07084765

Subjects
Primary: 53C20: Global Riemannian geometry, including pinching [See also 31C12, 58B20]
Secondary: 53C40: Global submanifolds [See also 53B25] 53A99: None of the above, but in this section

Citation

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


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References

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