Let S be a compact Sasakian manifold which does not admit nontrivial Hamiltonian holomorphic vector fields. If there exists an EinsteinSasakian metric on S, then it is unique.

The object of the present paper is to study the extended generalized φ-recurrent trans-Sasakian manifold and its various geometric properties.

A Sasakian structure S=(;;;;g) on a manifold M is called positive if its basic rst Chern class c 1 (F) can be represented by a positive (1;1)-form with respect to its transverse holomorphic CR-structure. We prove a theorem that says that every positive Sasakian structure can be deformed to a Sasakian structure whose metric has positive Ricci curvature. This allows us by example to give a comple...

We study the Lie algebra of infinitesimal isometries of 7–dimensional simply connected manifolds with Killing spinors. We obtain some splitting theorems for the action of this algebra on the space of Killing spinors, and as a corollary we prove that there are no infinitesimal isometry of constant length on a 7–dimensional 3– Sasakian manifold (not isometric to a space form) except the linear co...

We show that #9(S 2 S 3) admits an 8-dimensional complex family of inequivalent non-regular Sasakian-Einstein structures. These are the rst known Einstein metrics on this 5-manifold. In particular, the bound b 2 (M)8 which holds for any regular Sasakian-Einstein M does not apply to the non-regular case. We also discuss the failure of the Hitchin-Thorpe inequality in the case of 4-orbifolds and ...

Copyright q 2010 Siraj Uddin et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. We study warped product Pseudo-slant submanifolds of Sasakian manifolds. We prove a theorem for the existence of warped product submanifolds of a ...

The object of the present paper is to study generalized φ− recurrent and generalized concircular φ− recurrent P-Sasakian manifold. AMS Mathematics Subject Classification (2010): 53B20, 53D15.

In this paper, we give some sufficient conditions for semi– invariant product of a nearly Sasakian manifold, and generalize Bejancu’s result.

In this paper, we give some sufficient and necessary conditions for integrability of distribution D⊥ on a nearly Sasakian manifold, and generalize Bejancu’s result.

We show that the pseudohermitian sectional curvature Hθ(σ) of a contact form θ on a strictly pseudoconvex CR manifold M measures the difference between the lengthes of a circle in a plane tangent at a point of M and its projection on M by the exponential map associated to the Tanaka-Webster connection of (M, θ). Any Sasakian manifold (M, θ) whose pseudohermitian sectional curvature Kθ(σ) is a p...