In this paper, we introduce the notion of radical transversal screen Cauchy-Riemann (SCR)- lightlike submanifolds indefinite Sasakian manifolds giving characterization theorem with some nontrivial examples such submanifolds. Integrability conditions distributions D1, D2, D and D? on SCR-lightlike an manifold have been obtained. Further, obtain necessary sufficient for foliations determined by a...

In the papers [FS1], [FS2] we described some Siegel modular threefolds which admit a weak Calabi–Yau model.*) Not all of them admit a projective model. In fact, Bert van Geemen, in a private communication, pointed out a significative example which cannot admit a projective model. His comment was a starting motivation for this paper. We mention that a weak Calabi–Yau threefold is projective if, ...

1. Statement of the results. 1.1. Let M be a compact Kaehlerian manifold. The underlying Riemannian manifold which we also denote by M is orientable and of even dimension. Let K = K(<r) be the Riemannian curvature of M, considered as a Riemannian manifold. K(a) is a function on the 2planes a tangent to M. The restriction of K to holomorphic 2-planes is called holomorphic curvature and will be d...

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.

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...

Recently, we researched certain twisted product CR-submanifolds in a Kaehler manifold and some inequalities of the second fundamental form of this submanifold ([11]). In this talk, we consider two kind twisted product CR-submanifolds in a locally conformal Kaehler manifold. In these submanifolds, we give a inequality of the second fundamental form (See Theorems 5.3 and 5.4) and consider the equ...

By a symplectic manifold (or a symplectic n-fold) we mean a compact Kaehler manifold of even dimension n with a non-degenerate holomorphic 2form ω, i.e. ω is a nowhere-vanishing n-form. This notion is generalized to a variety with singularities. We call X a projective symplectic variety if X is a normal projective variety with rational Gorenstein singularities and if the regular locus U of X ad...