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