Let [Formula: see text] be a compact connected orientable Cauchy–Riemann (CR) manifold with the action of Lie group text]. Under natural pseudoconvexity assumptions we show that CR Guillemin–Sternberg map is an isomorphism at level Sobolev spaces functions, modulo finite-dimensional subspace. As application study this for holomorphic line bundles which are positive near inverse image by momentu...

This paper mainly devotes to the study of some solitons such as Ricci and Yamabe also their combination called Ricci-Yamabe solitons. In geometry solitons, a fundamental question is identify conditions under which these can be trivial. Firstly, in this we extensive results on generic contact CR-submanifolds Sasakian manifolds endowed with concurrent vector fields. Then applications submanifolds...

In this article, we investigate anti-invariant Riemannian and Lagrangian submersions onto manifolds from the Lorentzian para-Sasakian manifold. We demonstrate that, for these submersions, horizontal distributions are not integrable their fibers totally geodesic. As a result, they geodesic maps. The harmonicity of such is also examined. specifically prove that harmonic when Reeb vector field hor...

The purpose of this note is to introduce a new method for proving the existence of Sasakian-Einstein metrics on certain simply connected odd dimensional manifolds. We then apply this method to prove the existence of new Sasakian-Einstein metrics on S×S and on (S×S)#(S×S). These give the first known examples of non-regular Sasakian-Einstein 5manifolds. Our method involves describing the Sasakian...

Making use of the relations among 3-Sasakian manifolds, hypercomplex mani-folds and quaternionic KK ahler orbifolds, we prove that complete 3-Sasakian manifolds are rigid.

In this paper, we study the generalized m-quasi-Einstein metric in context of contact geometry. First, prove if an H-contact manifold admits a with non-zero potential vector field V collinear ?, then M is K-contact and ?-Einstein. Moreover, it also true when H-contactness replaced by completeness under certain conditions. Next, that complete closed whose thenMis compact, Einstein Sasakian. Fina...

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...