Related papers: Clairaut conformal submersions from Ricci solitons

We show that a complete Riemannian manifold has finite topological type (i.e., homeomorphic to the interior of a compact manifold with boundary), provided its Bakry-\'{E}mery Ricci tensor has a positive lower bound, and either of the…

We provide necessary and sufficient conditions for some particular couples $(g,\nabla)$ of pseudo-Riemannian metrics and affine connections to be statistical structures if we have gradient almost Einstein, almost Ricci, almost Yamabe…

In this paper, we have proved that if a complete conformally flat gradient shrinking Ricci soliton has linear volume growth or the scalar curvature is finitely integrable and also the reciprocal of the potential function is subharmonic,…

In the paper, we study complete almost Ricci solitons using the concepts and methods of geometric dynamics and geometric analysis. In particular, we characterize Einstein manifolds in the class of complete almost Ricci solitons. Then, we…

Let $(M^n, g, f)$, $n\geq 5$, be a complete gradient expanding Ricci soliton with nonnegative Ricci curvature $Rc\geq 0$. In this paper, we show that if the asymptotic scalar curvature ratio of $(M^n, g, f)$ is finite (i.e., $ \limsup_{r\to…

The aim of this paper is to study geometrical aspects of static spacetime admitting an almost gradient Ricci soliton. Among others, We first determine the conditions under which the base manifold of static spacetime possess an almost…

A Ricci soliton $(M^n,g,v,\lambda)$ on a Riemannian manifold $(M^n,g)$ is said to have concurrent potential field if its potential field $v$ is a concurrent vector field. In the first part of this paper we completely classify Ricci solitons…

In this paper, we establish a compactness theorem for gradient Ricci solitons with scalar curvature bounds and uniform lower bounds of harmonic coordinates. Our approach is to bootstrap regularity in harmonic coordinates by exploiting the…

In this paper, we first apply an integral identity on Ricci solitons to prove that closed locally conformally flat gradient Ricci solitons are of constant sectional curvature. We then generalize this integral identity to complete noncompact…

Conformal Ricci solitons are self similar solutions of the conformal Ricci flow equation. This paper deals with the study of conformal Ricci solitons within the framework of warped product manifolds which extends the notion of usual…

We investigate new Clairaut conditions for anti-invariant submersions from normal almost contact metric manifolds onto Riemannian manifolds. We prove that there is no Clairaut anti-invariant submersion admitting vertical Reeb vector field…

In the context of paracontact geometry, $\eta$-Ricci solitons are considered on manifolds satisfying certain curvature conditions: $(\xi,\cdot)_{R}\cdot S=0$, $(\xi,\cdot)_{S}\cdot R=0$, $(\xi,\cdot)_{W_2}\cdot S=0$ and…

Let $\overline{M}^{n+1}$ be a semi-Riemannian manifold of constant sectional curvature, and endowed with a conformal vector field . Consider a Riemannian manifold $M^n$, isometrically immersed into $\overline{M}^{n+1}$. With these…

In this paper, we study the following conjecture of Hamilton: Any compact gradient shrinking Ricci soliton with positive curvature operator must be Einstein. We first derive several identities. Then we show that the conjecture is true under…

In this research article, we establish the geometrical bearing on Riemannian submersions in terms of $\eta$-Ricci-Yamabe Soliton with the potential field and giving the classification of any fiber of Riemannian submersion is an…

The object of the present paper is to characterize the class of Kenmotsu manifolds which admits conformal $\eta$-Ricci soliton. Here, we have investigated the nature of the conformal $\eta$-Ricci soliton within the framework of Kenmotsu…

Geometrical aspects of a perfect fluid spacetime are described in terms of different curvature tensors and $\eta$-Ricci and $\eta$-Einstein solitons in a perfect fluid spacetime are determined. Conditions for the Ricci soliton to be steady,…

In this paper, we first show that a complete shrinking breather with Ricci curvature bounded from below must be a shrinking gradient Ricci soliton. This result has several applications. First, we can classify all complete $3$-dimensional…

The goal of our present paper is to deliberate $*$-conformal $\eta$-Ricci soliton within the framework of Kenmotsu manifolds. Here we have shown that a Kenmotsu metric as a $*$-conformal $\eta$-Ricci soliton is Einstein metric if the…

We consider almost $\eta$-Ricci solitons in $(\varepsilon)$-para Sasakian manifolds satisfying certain curvature conditions. In the gradient case we give an estimation of the Ricci curvature tensor's norm and express the scalar curvature of…