In this paper, we study 3-dimensional compact and connected trans-Sasakian manifolds find necessary sufficient conditions under which these are homothetic to Sasakian manifolds. First, four results in paper deal with finding on a manifold be manifold, the fifth result deals condition manifold. Finally, simply Einstein

A generalized flag manifold is a homogeneous space of the form G/K, where K is the centralizer of a torus in a compact connected semisimple Lie group G. We classify all flag manifolds with four isotropy summands by the use of t-roots. We present new G-invariant Einstein metrics by solving explicity the Einstein equation. We also examine the isometric problem for these Einstein metrics. 2000 Mat...

Recently it was conjectured that parallel branes at conical singularities are related to string/M theory on AdS×X where X is an Einstein manifold. In this paper we consider coincident M2 branes near a conifold singularity when M theory is compactified on AdS4×Q for Q = (SU(2)×SU(2)× SU(2))/(U(1)× U(1)) as a seven dimensional Sasaki-Einstein manifold. We argue that M theory on AdS4 × Q can be de...

In the context of paracontact geometry, η-Ricci solitons are considered on manifolds satisfying certain curvature conditions: R(ξ,X) · S = 0, S · R(ξ,X) = 0, W2(ξ,X) · S = 0 and S · W2(ξ,X) = 0. We prove that on a para-Kenmotsu manifold (M,φ, ξ, η, g), the existence of an η-Ricci soliton implies that (M, g) is quasi-Einstein and if the Ricci curvature satisfies R(ξ,X) · S = 0, then (M, g) is Ei...

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...

The object of the present paper is to characterize class Kenmotsu manifolds which admits conformal $$\eta $$ -Ricci soliton. Here, we have investigated nature soliton within framework manifolds. It shown that an -Einstein manifold admitting Einstein one. Moving further, considered gradient on and established a relation between potential vector field Reeb field. Next, it proved under certain con...