Existence of flats in manifolds of nonpositive curvature
The authors prove that the existence of an immersed m-flat in a compact Riemannian manifold of nonpositive sectional curvature depends only on the fundamental group of the manifold. The proof uses methods from geometric measure theory. Recall that the existence of a 2-flat is equivalent to non-visibility, as was shown by elementary means by P. Eberlein.
scientific article; zbMATH DE number 3996556
scientific article