Random Manifolds have no Totally Geodesic Submanifolds
Differential Geometry
2018-01-19 v2
Abstract
For we show that generic closed Riemannian -manifolds have no nontrivial totally geodesic submanifolds, answering a question of Spivak. An immediate consequence is a severe restriction on the isometry group of a generic Riemannian metric. Both results are widely believed to be true, but we are not aware of any proofs in the literature.
Cite
@article{arxiv.1703.09240,
title = {Random Manifolds have no Totally Geodesic Submanifolds},
author = {Thomas Murphy and Frederick Wilhelm},
journal= {arXiv preprint arXiv:1703.09240},
year = {2018}
}
Comments
V2: minor changes to address referees' reports, calculations in the local construction have been made more explicit. To appear in Michigan Math. J