Several uniqueness results for non-compact complete stationary spacelike surfaces in an $$n(\ge 3)$$ -dimensional Generalized Robertson Walker spacetime are obtained. In order to do that, we assume a natural inequality involving the Gauss curvature of surface, restrictions warping function and sectional fiber surface. This gives parabolicity Using this property, distinguished non-negative super...

We obtain the expressions for sectional curvature, holomorphic sectional curvature, and holomorphic bisectional curvature of a GCR-lightlike submanifold of an indefinite Kaehler manifold. We discuss the boundedness of holomorphic sectional curvature of GCR-lightlike submanifolds of an indefinite complex space form. We establish a condition for a GCR-lightlike submanifold of an indefinite comple...

in the first part of this paper, some theorems are given for a riemannian manifold with semi-symmetric metric connection. in the second part of it, some special vector fields, for example, torse-forming vector fields, recurrent vector fields and concurrent vector fields are examined in this manifold. we obtain some properties of this manifold having the vectors mentioned above.

Let M be a complete Riemannian locally symmetric space of nonpositive curvature and of finite volume. We show that there are only finitely many compact maximal flats in M of volume bounded by a given number. As a corollary in the case M = SLn(Z)\ SLn(R)/ SOn, we give a different proof of a theorem of Remak that for any n ∈ N, there are only finitely many totally real number fields of degree n w...

On a 3-dimensional Lorentzian manifold, the sectional curvature function at any point may be represented as a rational function (quotient of two quadratics) on the real projective plane [2]. (More generally, the sectional curvature at a point of any pseudoRiemannian n-manifold may be represented as a rational function on the Grassmann variety of planes in n-space.) Using this representation, Be...

We construct a continuous family of new homogeneous Einstein spaces with negative Ricci curvature, obtained by deforming from the quaternionic hyperbolic space of real dimension 12. We give an explicit description of this family, which is made up of Einstein solvmanifolds which share the same algebraic structure (eigenvalue type) as the rank one symmetric space HH. This deformation includes a c...

In this paper we study some rigidity properties for Finsler manifolds of sectional flag curvature. We prove that any Landsberg manifold of non-zero sectional flag curvature and any closed Finsler manifold of negative sectional flag curvature must be Riemannian.