In this paper, we study the geometry of a semi-Riemannian manifold M̄ of quasi-constant curvature. The main result is two characterization theorems for M̄ endowed with a statical, screen homothetic or screen totally umbilical half lightlike submanifold M . Mathematics Subject Classification: 53C25, 53C40, 53C50

We study umbilic (space-like) submanifolds of pseudo-Riemannian space forms, then define totally semi-umbilic space-like submanifold of pseudo Euclidean space and relate this notion to umbilicity. Finally we give characterization of total semi-umbilicity for space-like submanifolds contained in pseudo sphere or pseudo hyperbolic space or the light cone.A pseudo-Riemannian submanifold M in (a...

In this paper, we would like to study space-like submanifolds in a de Sitter spaces S p (1). We define and discuss three Schrödinger operators LH , LR, LR/H and obtain some spectral characterizations of totally umbilical space-like submanifolds in terms of the first eigenvalue of the Schrödinger operators LH , LR and LR/H respectively.

In this paper we study existence and lack thereof of closed embedded orientable co-dimension one totally geodesic submanifolds minimal volume cusped hyperbolic manifolds.

This paper gives a complete parametrization of the commensurability classes of totally geodesic subspaces of irreducible arithmetic quotients of Xa,b = (H ) × (H). A special case describes all Shimura subvarieties of type A1 Shimura varieties. We produce, for any n ≥ 1, examples of manifolds/Shimura varieties with precisely n commensurability classes of totally geodesic submanifolds/Shimura sub...