2017/03/27 by Thomas E. Murphy, Murphy, Thomas, Frederick Wilhelm +1
Mathematics · Computer Science · #Geometric Analysis and Curvature Flows #Morphological variations and asymmetry #Topological and Geometric Data Analysis
paper · pdf · doi:10.48550/arxiv.1703.09240
For n≥ 4 we show that generic closed Riemannian n-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.