We prove the following results: (i) A Sasakian metric as a nontrivial Ricci soliton is null η-Einstein, and expanding. Such a characterization permits to identify the Sasakian metric on the Heisenberg group H as an explicit example of (non-trivial) Ricci soliton of such type. (ii) If an ηEinstein contact metric manifold M has a vector field V leaving the structure tensor and the scalar curvatur...

We construct exact solutions of the Einstein-Dirac equation, which couples the gravitational eld with an eigenspinor of the Dirac operator via the energy-momentum tensor. For this purpose we introduce a new eld equation generalizing the notion of Killing spinors. The solutions of this spinor eld equation are called weak Killing spinors (WK-spinors). They are special solutions of the Einstein-Di...

Many authors have studied Ricci solitons and their analogs within the framework of (almost) contact geometry. In this article, we thoroughly study $$(m,\rho )$$ -quasi-Einstein structure on a metric manifold. First, prove that if K-contact or Sasakian manifold $$M^{2n+1}$$ admits closed structure, then it is an Einstein constant scalar curvature $$2n(2n+1)$$ , for particular case—a non-Sasak...

In this article, the properties of projective, concircular and conharmonic curvature tensor fields on a complex Sasakian manifold are investigated.

The purpose of this study is to evaluate the curvature tensor and Ricci a P-Sasakian manifold with respect quarter-symmetric metric connection on tangent bundle TM. Certain results semisymmetric manifold, generalized recurrent manifolds, pseudo-symmetric manifolds TM are proved.

We prove a CR version of the Obata’s result for the first eigenvalue of the sub-Laplacian in the setting of a compact strictly pseudoconvex pseudohermitian three dimensional manifold with non-negative CR-Paneitz operator which satisfies a Lichnerowicz type condition. We show that if the first positive eigenvalue of the sub-Laplacian takes the smallest possible value then, up to a homothety of t...

In this study, we introduce indefinite sasakian statistical manifolds and lightlike hypersurfaces of an manifold. Some relations among induced geometrical objects with respect to dual connections in a hypersurface manifold are obtained. examples related these concepts also presented. Finally, prove that invariant submanifold is

In this paper we prove the existence of Einstein metrics, actually SasakianEinstein metrics, on nontrivial rational homology spheres in all odd dimensions greater than 3. It appears as though little is known about the existence of Einstein metrics on rational homology spheres, and the known ones are typically homogeneous. The are two exception known to the authors. Both involve Sasakian geometr...

The geometry of nearly trans-Sasakian manifolds is researched in this paper. complete group structural equations and the components Lee vector on space associated $G$-structure are obtained for such manifolds. Conditions found under which a structure trans-Sasakian, cosymplectic, closely Sasakian or Kenmotsu structure. conditions when special generalized second kind. A classification obtained, ...

We prove a CR version of the Obata’s result for the first eigenvalue of the sub-Laplacian in the setting of a compact strictly pseudoconvex pseudohermitian manifold which satisfies a Lichnerowicz type condition and has a divergence free pseudohermitian torsion. We show that if the first positive eigenvalue of the sub-Laplacian takes the smallest possible value then, up to a homothety of the pse...