The aim of this paper is to study the stability of the characteristic vector field of a compact K-contact manifold with respect to the energy and volume functionals when we consider on the manifold a two-parameter variation of the metric. First of all, we multiply the metric in the direction of the characteristic vector field by a constant and then we change the metric by homotheties. We will s...

Sasakian manifolds are odd-dimensional counterpart to Kähler manifolds. They can be defined as contact equipped with an invariant structure on their symplectic cone. The quotient of this cone by the homothety action is a complex manifold called Vaisman. We study harmonic forms and Hodge decomposition Vaisman construct Lie superalgebra associated in same way supersymmetry algebra manifold. use c...

for arbitrary vector fieldsX, Y , Z, U , V ∈ χ(Mn), whereD denotes the operator of covariant differentiation with respect to the Riemannian metric g and A, B, C, D and E are 1−forms (not simultaneously zero). The 1−forms are called the associated 1−forms of the manifold and an n−dimensional manifold of this kind is denoted by (WS)n. Tamassy and Binh [14] further studied weakly symmetric Sasakia...

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

Purpose The authors set the goal to find solution of Eisenhart problem within framework three-dimensional trans-Sasakian manifolds. Also, they prove some results Ricci solitons, η -Ricci solitons and weakly  symmetric Finally, give a nontrivial example proper manifold. Design/methodology/approach ha...

Recently, the authors [BG2] introduced a new method for showing the existence of Sasakian-Einstein metrics on compact simply connected 5-dimensional spin manifolds. This method was based on work of Demailly and Kollár [DK] who gave sufficient algebraic conditions on log del Pezzo surfaces anticanonically embedded in weighted projective spaces to guarantee the existence of a Kähler-Einstein orbi...

As a generalization of semi-invariant $\xi ^{\perp }$-Riemannian submersions, we introduce the generic }$- Riemannian submersions. We focus on submersions for Sasakian manifolds with examples and investigate geometry foliations. Also, necessary sufficient conditions base manifold to be local product are obtained new totally geodesicity established. Furthermore, curvature properties distribution...