The object of the present paper is to characterize Cotton tensor on a 3-dimensional Sasakian manifold admitting $\eta$-Ricci solitons. After introduction, we study manifolds and introduce new notion, namely, pseudo-symmetric manifolds. Next deal with 3-manifold Among others prove that such constant scalar curvature Einstein some appropriate conditions. Also, classify nature soliton metric. Fina...

We consider almost Riemann solitons $$(V,\lambda )$$ in a Riemannian manifold and underline their relation to Ricci solitons. When V is of gradient type, using Bochner formula, we explicitly express the function $$\lambda $$ by means vector field illustrate result with suitable examples. Moreover, deduce some properties for particular cases when potential soliton solenoidal or torse-forming, sp...

We obtain on a Kähler B-manifold (i.e., manifold with Norden metric) some corresponding results from the Kählerian and para-Kählerian context concerning Bochner curvature. prove that such is of constant totally real sectional curvatures if only it holomorphic Einstein, flat manifold. Moreover, we provide necessary sufficient conditions for gradient Ricci soliton or ?-Einstein metric to be flat....

Walker manifolds of signature (2, 2) have been used by many authors to provide examples of Osserman and of conformal Osserman manifolds of signature (2, 2). We study questions of geodesic completeness and Ricci blowup in this context.

Abstract We derive a sharp lower bound for the scalar curvature of non-flat and non-compact expanding gradient Ricci soliton provided that is non-negative potential function proper. Upper expander with nonpositive will also be given. Furthermore, we provide sufficient condition being non-negative. Curvature estimates solitons in dimensions three four established. As an application, prove gap th...

We derive a local ansatz for generalized K\"ahler surfaces with nondegenerate Poisson structure and biholomorphic $S^1$ action which generalizes the classic Gibbons-Hawking invariant hyperK\"ahler manifolds, allows choice of one arbitrary function. By imposing K\"ahler-Ricci soliton equation, or equivalently equations type IIB string theory, construction becomes rigid, we classify all complete ...

The main aim of this article is to provide a lower bound the diameter compact gradient ?-Einstein soliton satisfying some given conditions. We have also deduced conditions with bounded Ricci curvature become non-shrinking and non-expanding. Further, we proved that complete non-compact shrinking or expanding Schouten non-constant potential along condition for boundedness scalar must be non-parab...

We characterize the Einstein metrics in such broad classes of as almost $$\eta $$ -Ricci solitons and on Kenmotsu manifolds, generalize some known results. First, we prove that a metric an soliton is if either it -Einstein or potential vector field V infinitesimal contact transformation collinear to Reeb field. Further, manifold admits gradient with leaving scalar curvature invariant, then mani...

The target of the current research article is to investigate solitonic attributes relativistic magneto-fluid spacetime (MFST) if its metrics are Ricci–Yamabe soliton (RY-soliton) and gradient (GRY-soliton). We exhibit that a filled with density ρ, magnetic field strength H, permeability μ obeys Einstein equation without cosmic constant being generalized quasi-Einstein manifold (GQE). In such sp...

Let $(X, D)$ be a log variety with an effective holomorphic torus action, and $\Theta$ closed positive $(1,1)$-current. For any smooth function $g$ defined on the moment polytope of we study Monge-Amp\`{e}re equations that correspond to generalized twisted K\"{a}hler-Ricci $g$-solitons. We prove version Yau-Tian-Donaldson (YTD) conjecture for these general equations, showing existence solutions...