On Semiparallel and Weyl-semiparallel Hypersurfaces of Kaehler Manifolds

Lecture on Kaehler manifolds

Hopf hypersurfaces in nearly Kaehler 6-sphere

We obtain a characterization for a compact Hopf hypersurface in the nearly Kaehler sphere S using a pinching on the scalar curvature of the hypersurface. It has been also observed that the totally geodesic sphere S in S has induced Sasakian structure as a hypersurface of the nearly Kaehler sphere S. M.S.C. 2000: 53C20, 53C45.

Ricci tensor for $GCR$-lightlike submanifolds of indefinite Kaehler manifolds

We obtain the expression of Ricci tensor for a $GCR$-lightlikesubmanifold of indefinite complex space form and discuss itsproperties on a totally geodesic $GCR$-lightlike submanifold of anindefinite complex space form. Moreover, we have proved that everyproper totally umbilical $GCR$-lightlike submanifold of anindefinite Kaehler manifold is a totally geodesic $GCR$-lightlikesubmanifold.

Conformal mappings preserving the Einstein tensor of Weyl manifolds

In this paper, we obtain a necessary and sufficient condition for a conformal mapping between two Weyl manifolds to preserve Einstein tensor. Then we prove that some basic curvature tensors of $W_n$ are preserved by such a conformal mapping if and only if the covector field of the mapping is locally a gradient. Also, we obtained the relation between the scalar curvatures of the Weyl manifolds r...

Some Submersions of Cr-hypersurfaces of Kaehler-einstein Manifold

The Riemannian submersions of a CR-hypersurface M of a Kaehler-Einstein man-ifold˜M are studied. If M is an extrinsic CR-hypersurface of˜M, then it is shown that the base space of the submersion is also a Kaehler-Einstein manifold. 1. Introduction. The study of the Riemannian submersions π : M → B was initiated by O'Neill [14] and Gray [9]. This theory was very much developed in the last thirty...