The Michigan Mathematical Journal
- Michigan Math. J.
- Volume 68, Issue 2 (2019), 323-335.
Random Manifolds Have No Totally Geodesic Submanifolds
For , we show that generic closed Riemannian -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.
Michigan Math. J., Volume 68, Issue 2 (2019), 323-335.
Received: 25 May 2017
Revised: 17 January 2018
First available in Project Euclid: 12 April 2019
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
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