Abstract A well-known application of the Raychaudhuri equation shows that, under geodesic completeness, totally null hypersurfaces are unique which satisfy that Ricci curvature is nonnegative in direction. The proof this fact based on a direct analysis differential inequality. In paper, we show, without assuming an inequality involving squared mean and compact three-dimensional hypersurface als...

The present article is the final part of a series on the classification of the totally geodesic submanifolds of the irreducible Riemannian symmetric spaces of rank 2. After this problem has been solved for the 2-Grassmannians in my papers [K1] and [K2], and for the space SU(3)/SO(3) in Section 6 of [K3], we now solve the classification for the remaining irreducible Riemannian symmetric spaces o...

It is shown that every non-compact hyperbolic manifold of finite volume has a finite cover admitting a geodesic ideal triangulation. Also, every hyperbolic manifold of finite volume with non-empty, totally geodesic boundary has a finite regular cover which has a geodesic partially truncated triangulation. The proofs use an extension of a result due to Long and Niblo concerning the separability ...