Related papers: From harmonic mappings to Ricci solitons
Harmonic morphisms are maps between Riemannian manifolds that pull back harmonic functions to harmonic functions. These maps are characterized as horizontally weakly conformal harmonic maps and they have many interesting links and…
The object of the present paper is to study some types of Ricci pseudosymmetric $(LCS)_n$-manifolds whose metric is Ricci soliton. We found the conditions when Ricci soliton on concircular Ricci pseudosymmetric, projective Ricci…
In this paper, it is elaborated the theory the Ricci flows for manifolds enabled with nonintegrable (nonholonomic) distributions defining nonlinear connection structures. Such manifolds provide a unified geometric arena for nonholonomic…
We give a geometric interpretation of Hamilton's matrix Harnack inequality for the Ricci flow as the curvature of a connection on space-time.
The purpose of this article is to study implications of a Ricci soliton warped product manifold to its base and fiber manifolds. First, it is proved that if a warped product manifold is Ricci soliton then its factors are Ricci soliton. Then…
This note reviews some of the recent work on biharmonic conformal maps (see \cite{OC}, Chapter 11, for a detailed survey). It will be focused on biharmonic conformal immersions and biharmonic conformal maps between manifolds of the same…
The purpose of the article is to study a foliation associated to a lattice-equivariant harmonic map of small rank from a complex ball to another. The result is related to rigidity of some complex ball quotients.
In this paper we study the gradient Ricci shrinking soliton equation on rotationally symmetric manifolds of dimension three and higher and prove that the only complete examples of such metrics on $S^n$, $\R{n}$ and $\R{}\times S^{n-1}$ are,…
I discuss certain applications of the Ricci flow in physics. I first review how it arises in the renormalization group (RG) flow of a nonlinear sigma model. I then review the concept of a Ricci soliton and recall how a soliton was used to…
We investigate transverse Ricci solitons, the self-similar solutions of the transverse Ricci flow, on a compact foliated manifold. In particular, we show the relations between a taut Riemannian foliation and a transverse Ricci soliton.…
In this paper, we study conformal Ricci solitons and conformal gradient Ricci solitons on generalized ($\kappa,\mu$)-space forms. The conditions for the solitons to be shrinking, steady, and expanding are derived in terms of conformal…
This article reports recent developments of the research on Hamilton's Ricci flow and its applications.
A complete study of the structure of Ricci collineations for type B warped spacetimes is carried out. This study can be used as a method to obtain these symetries in such spacetimes. Special cases as 2+2 reducible spacetimes, and plane and…
We consider four-dimensional homogeneous pseudo-Riemannian manifolds with non-trivial isotropy and completely classify the cases giving rise to non-trivial homogeneous Ricci solitons. In particular, we show the existence of non-compact…
This paper explores the evolution and monotonicity of geometric constants within the framework of extended Ricci flows, incorporating variable coupling parameters. Building on Hamiltons foundational Ricci flow and subsequent extensions by…
We study the infinitesimal rigidity of equivariant minimal maps from the universal cover of a smooth oriented surface (possibly non-compact) into a Riemannian symmetric space, focusing on representations arising from cyclic harmonic…
In this text, we are concerned with ring epimorphisms, and more specifically universal localisations, from path algebras to matrix algebras. We are mainly focused on constructing ring epimorphisms and universal localisations by extending…
Harmonic maps from $\BR^2$ or one-connected domain ${\O}\subset \BR^2$ into $GL(m, \BC)$ and $U(m)$ are treated. The GBDT version of the B\"acklund-Darboux transformation is applied to the case of the harmonic maps. A new general formula on…
The Eisenhart problem of finding parallel tensors treated already in the framework of quasi-constant curvature manifolds in \cite{x:j} is reconsidered for the symmetric case and the result is interpreted in terms of Ricci solitons. If the…
We introduce and study $H$-paracontact metric manifolds, that is, paracontact metric manifolds whose Reeb vector field $\xi$ is harmonic. We prove that they are characterized by the condition that $\xi$ is a Ricci eigenvector. We then…