Totally geodesic hypersurfaces in manifolds of nonpositive curvature (Q1345755)

Let \(X\) be the universal covering space of a compact Riemannian manifold \(M\) of nonpositive sectional curvature \(K_M\). Let \(P\) be a totally geodesic hypersurface in \(X\). The authors discuss the possible structures for \(X\) and \(P\) in the case that the projection of \(P\) to \(X\) does not have selfintersections with arbitrarily small angles. They obtain for example that the projection of \(P\) has to be compact if it does not have selfintersections with arbitrarily small angles and \(\dim M \geq 3\), \(K_M < 0\).