## The Michigan Mathematical Journal

### Random Manifolds Have No Totally Geodesic Submanifolds

#### Abstract

For $n\geq 4$, 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
Revised: 17 January 2018
First available in Project Euclid: 12 April 2019

https://projecteuclid.org/euclid.mmj/1555034652

Digital Object Identifier
doi:10.1307/mmj/1555034652

Mathematical Reviews number (MathSciNet)
MR3961219

Zentralblatt MATH identifier
07084765

#### 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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