The goal of the current paper is to characterize $*$-$k$-Ricci-Yamabe soliton within framework on Kenmotsu manifolds. Here, we have shown nature and find scalar curvature when manifold admitting manifold. Next, evolved characterization vector field satisfies soliton. Also embellished some applications as torse-forming in terms Then, studied gradient $\ast$-$\eta$-Einstein yield Riemannian tenso...

We define a Hesse soliton, that is, self-similar solution to the flow on Hessian manifolds. On information geometry, e-connection is important, which does not coincide with Levi–Civita one. Therefore, it interesting consider manifold flat connection call proper manifold. In this paper, we show any compact soliton expanding and non-trivial gradient proper. Furthermore, dual space of Hesse–Einste...

We introduce and study a new type of soliton with potential Reeb vector field on Riemannian manifolds an almost paracontact structure corresponding to paracomplex structure. The special cases para-Einstein-like, para-Sasaki-like having torse-forming were considered. It was proved necessary sufficient condition for the manifold admit para-Ricci-like soliton, which is that para-Einstein-like. Exp...

We analyse in a systematic way the (non-)compact n-dimensional Einstein-Weyl spaces equipped with a cohomogeneity-one metric. In that context, with no compactness hypothesis for the manifold on which lives the Einstein-Weyl structure, we prove that, as soon as the (n-1)-dimensional space is a homogeneous reductive Riemannian space with a unimodular group of left-acting isometries G : • there ex...

We show that for every positive curvature Kähler–Einstein manifold in dimension 2n there is a countably infinite class of associated Sasaki– Einstein manifolds X2n+3 in dimension 2n + 3. When n = 1 we recover a recently discovered family of supersymmetric AdS5 × X5 solutions of type IIB string theory, while when n = 2 we obtain new supersymmetric AdS4×X7 solutions of D = 11 supergravity. Both a...

If M is the underlying smooth oriented 4-manifold of a Del Pezzo surface, we consider the set of Riemannian metrics h on M such that W(ω, ω) > 0, where W is the self-dual Weyl curvature of h, and ω is a non-trivial self-dual harmonic 2-form on (M,h). While this open region in the space of Riemannian metrics contains all the known Einstein metrics on M , we show that it contains no others. Conse...

The paper undertakes certain special forms of the quarter symmetric metric and non-metric connections on an ε-anti-Kähler manifold. Firstly, we deduce relation between Riemannian connection connections. Then, present some results concerning torsion tensors these In addition, find curvature tensor, Ricci tensor scalar such search conditions for manifold to be Einstein space with respect Finally,...