Let N be the class of closed simply connected, smooth n–manifolds that admit nonnegative sectional curvature and let P be the corresponding class for positive curvature. Known examples suggest that N ought to be much larger than P . On the other hand, there is no known obstruction that distinguishes between the two classes. So its actually possible that N = P . In [PetWilh2] we will give a defo...

In this article we investigate the geometry of CR-lightlike submanifolds in an indefinite Kähler product manifold. In particular, we obtain the necessary and sufficient conditions for a CR-lightlike submanifold in an indefinite Kähler product manifold to be either CR-lightlike product, or D-geodesic, or D′-geodesic. We also study totally umbilical and curvature-invariant CR-lightlike submanifol...

Exact metrics on some totally geodesic submanifolds of the moduli space of static hyperbolic N -vortices are derived. These submanifolds, denoted Σn,m, are spaces of Cn-invariant vortex configurations with n single vortices at the vertices of a regular polygon and m = N − n coincident vortices at the polygon’s centre. The geometric properties of Σn,m are investigated, and it is found that Σn,n−...

The classical Cartan-Hadamard theorem asserts that a closed Riemannian manifold M with non-positive sectional curvature has universal cover M̃ diffeomorphic to R, and a byproduct of the proof is that ∂∞M̃n is homeomorphic to Sn−1. We prove analogues of these two results in the case where M has a non-empty totally geodesic boundary. More precisely, if M 1 ,M n 2 are two negatively curved Riemannia...

The object of this paper is to study invariant submanifolds M of Kenmotsu manifolds M̃ admitting a quarter symmetric metric connection and to show that M admits quarter symmetric metric connection. Further it is proved that the second fundamental forms σ and σ with respect to LeviCivita connection and quarter symmetric metric connection coincide. Also it is shown that if the second fundamental f...

We consider the decomposition of a compact-type symmetric space into a product of factors and show that the rank-one factors, when considered as totally geodesic submanifolds of the space, are isolated from inequivalent minimal submanifolds.

In this study, notion of pluriharmonic map applied onto conformal bi-slant Riemannian maps from a Kaehler manifold to examine its geometric properties. Such that, relations between map, horizontally homothetic and totally geodesic were obtained.

In this article, we investigate anti-invariant Riemannian and Lagrangian submersions onto manifolds from the Lorentzian para-Sasakian manifold. We demonstrate that, for these submersions, horizontal distributions are not integrable their fibers totally geodesic. As a result, they geodesic maps. The harmonicity of such is also examined. specifically prove that harmonic when Reeb vector field hor...