Related papers: Clairaut conformal submersions from Ricci solitons

Pro and the third author showed that there are Riemannian submersions $\pi: M \to B$ with $M$ a compact manifold with positive Ricci curvature, whose base $B$, has Ricci curvatures with both signs. Thus, Riemannian submersions need not…

Let $(M, g, f)$ be a $4$-dimensional complete noncompact gradient shrinking Ricci soliton with the equation $Ric+\nabla^2f=\lambda g$, where $\lambda$ is a positive real number. We prove that if $M$ has constant scalar curvature…

We consider smooth Riemannian surfaces whose curvature $K$ satisfies the relation $\Delta\log|K-c|=aK+b$ away from points where $K=c$ for some $(a,b,c)\in\mathbb{R}^3$, which we call generalized Ricci surfaces. We prove some isometric…

In this paper, we study constant weighted mean curvature hypersurfaces in shrinking Ricci solitons. First, we show that a constant weighted mean curvature hypersurface with finite weighted volume cannot lie in a region determined by a…

Among other results, a compact almost K\"ahler manifold is proved to be K\"ahler if the Ricci tensor is semi-negative and its length coincides with that of the star Ricci tensor or if the Ricci tensor is semi-positive and its first order…

Suppose $(M^n, g, f)$ is a complete shrinking gradient Ricci soliton. We give several rigidity results under some natural conditions, generalizing the results in \cite{Petersen-Wylie,Guan-Lu-Xu}. Using maximum principle, we prove that…

In this paper we introduce the notion of Einstein-type structure on a Riemannian manifold $\varrg$, unifying various particular cases recently studied in the literature, such as gradient Ricci solitons, Yamabe solitons and quasi-Einstein…

We consider almost Riemann and almost Ricci solitons in a $D$-homothetically deformed Kenmotsu manifold having as potential vector field a gradient vector field, a solenoidal vector field or the Reeb vector field of the deformed structure,…

We provide conditions for a compact gradient hyperbolic Ricci and a compact gradient hyperbolic Yamabe soliton to be trivial, hence, the manifold to be an Einstein manifold in the first case, and a manifold of constant scalar curvature, in…

In this paper the notion of Ricci $\rho$-soliton as a generalization of Ricci soliton is defined. We are motivated by the Ricci-Bourguignon flow to define this concept. We show that if a 3- dimensional almost Kenmotsu Einstein manifold $M$…

A Killing submersion is a Riemannian submersion from a 3-manifold to a surface, both connected and orientable, whose fibres are the integral curves of a Killing vector field, not necessarily unitary. The first part of this paper deals with…

We investigate four-dimensional gradient shrinking Ricci solitons with positive modified sectional curvature. Our first main result shows that if the norm of the self-dual Weyl tensor and the scalar curvature satisfy a certain sharp…

In [Cheeger-Tian 2005], Cheeger-Tian proved an $\epsilon$-regularity theorem for $4$-dimensional Einstein manifolds without volume assumption. They conjectured that similar results should hold for critical metrics with constant scalar…

In this paper we study certain types of metrics such as Ricci soliton, $*$-conformal Ricci soliton in 3-dimensional trans-Sasakian manifold. First we have shown that a 3-dimensional trans-Sasakian manifold of type $(\alpha,\beta)$ admits a…

Thurston's triangulation conjecture asserts that every hyperbolic 3-manifold admits a geometric triangulation into hyper-ideal hyperbolic tetrahedra. So far, this conjecture had only been proven for a few special 3-manifolds. In this…

We consider a problem of prescribing the partial Ricci curvature on a locally conformally flat manifold $(M^n, g)$ endowed with the complementary orthogonal distributions $D_1$ and $D_2$. We provide conditions for symmetric $(0,2)$-tensors…

In this paper, we prove that any $\kappa$-noncollapsed gradient steady Ricci soliton with nonnegative curvature operator and horizontally $\epsilon$-pinched Ricci curvature must be rotationally symmetric. As an application, we show that any…

In this paper, we give a delay estimate of scalar curvature for a complete non-compact expanding (or steady) gradient Ricci soliton with nonnegative Ricci curvature. As an application, we prove that any complete non-compact expanding (or…

We show that for an $n$ dimensional complete non Ricci flat gradient steady Ricci soliton with potential function $f$ bounded above by a constant and curvature tensor $Rm$ satisfying $\overline{\lim}_{r\to \infty} r|Rm|<\frac{1}{5}$, then…

In this paper, we begin by introducing Clairaut Riemannian warped product maps and establish the condition under which a regular curve becomes a geodesic. We obtain the conditions for a Riemannian warped product map to be Clairaut…