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 present paper, we have studied M -projectively flat generalized Sasakian space form, η-Einstein generalized Sasakian space form and irrotational M -projective curvature tensor on a Sasakian space form.

Let (M, g) be a Riemannian spin manifold. The basic equations in supergravity models of type IIa string theory with 4-form flux involve a 3-form T , a 4-form F , a spinorial covariant derivative ∇ depending on ∇, T , F , and a ∇-parallel spinor field Ψ. We classify and construct many explicit families of solutions to this system of spinorial field equations by means of non-integrable special ge...

We give an overview of some recent results in hypersymplectic and para-quaternionic Kähler geometry, and introduce the notion of split three-Sasakian manifold. In particular, we discuss the twistor spaces and Swann bundles of para-quaternionic Kähler manifolds. These are used to classify examples with a fully homogeneous action of a semi-simple Lie group, and to construct distinct para-quaterni...

Let M be a compact locally conformal hyperkähler manifold. We prove a version of Kodaira-Nakano vanishing theorem for M . This is used to show that M admits no holomorphic differential forms, and the cohomology of the structure sheaf H(OM ) vanishes for i > 1. We also prove that the first Betti number of M is 1. This leads to a structure theorem for locally conformally hyperkähler manifolds, de...