The object of the present paper is to study 3-dimensional trans-Sasakian manifolds admitting a W2-curvature tensor. Trans-Sasakian manifolds satisfying the curvature condition S(X, ξ).R = 0 is also considered.

We study lightlike hypersurfaces of para-Sasakian manifolds tangent to the characteristic vector field. In particular, we define invariant lightlike hypersurfaces and screen semi-invariant lightlike hypersurfaces, respectively, and give examples. Integrability conditions for the distributions on a screen semi-invariant lightlike hypersurface of para-Sasakian manifolds are investigated. We obtai...

We study Ricci solitons in Lorentzian α-Sasakian manifolds. It is shown that a symmetric parallel second order covariant tensor in a Lorentzian α-Sasakian manifold is a constant multiple of the metric tensor. Using this it is shown that if LV g + 2S is parallel, V is a given vector field then (g, V ) is Ricci soliton. Further, by virtue of this result Ricci solitons for (2n + 1)-dimensional Lor...

The aim of the present paper is to study properties of Quasi conformally flat LP-Sasakian manifolds with a coefficient α. In this paper, we prove that a Quasi conformally flat LP-Sasakian manifold M (n > 3) with a constant coefficient α is an η−Einstein and in a quasi conformally flat LP-Sasakian manifold M (n > 3) with a constant coefficient α if the scalar curvature tensor is constant then M ...

We give a formula for the Betti numbers of 3-Sasakian manifolds or orbifolds which can be obtained as 3-Sasakian quotients of a sphere by a torus. This answers a question of Galicki and Salamon about the topology of 3-Sasakian manifolds. A (4m+3)-dimensional manifold is 3-Sasakian if it possesses a Riemannian metric with three orthonormal Killing elds deening a local SU(2)-action and satisfying...

We obtain a basic inequality involving the Laplacian of the warping function and the squared mean curvature of any warped product isometrically immersed in a Riemannian manifold (cf. Theorem 2.2). Applying this general theory, we obtain basic inequalities involving the Laplacian of the warping function and the squared mean curvature of C-totally real warped product submanifolds of (κ, μ)-space ...

In the present paper we studied the properties of them−projective curvature tensor in LP-Sasakian, Einstein LP-Sasakian and η−Einstein LPSasakian manifolds.

A compact quasi-regular Sasakian manifold M is foliated by onedimensional leaves and the transverse space of this characteristic foliation is necessarily a compact Kähler orbifold Z. In the case when the transverse space Z is also Einstein the corresponding Sasakian manifold M is said to be Sasakian η-Einstein. In this article we study η-Einstein geometry as a class of distinguished Riemannian ...

This paper describes certain hypercomplex manifolds as circle V-bundles over 3-Sasakian orbifolds. Our techniques involve both 3-Sasakian and hypercomplex reduction. In general dimension most of the quotients exist only as hypercomplex orbifolds; however, we construct a large family of compact simply connected smooth 8-manifolds whose second integral homology group is free with arbitrary rank. ...