Related papers: From harmonic mappings to Ricci solitons

We characterize $\eta$-Ricci solitons $(g,\xi,\lambda,\mu)$ in some special cases when the $1$-form $\eta$, which is the $g$-dual of $\xi$, is a harmonic or a Schr\"{o}dinger-Ricci harmonic form. We also provide necessary and sufficient…

We establish a 1-to-1 relation between metrics on compact Riemann surfaces without boundary, and mechanical systems having those surfaces as configuration spaces.

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…

Conformal harmonic maps from a 4-dimensional conformal manifold to a Riemannian manifold are maps satisfying a certain conformally invariant fourth order equation. We prove a general existence result for conformal harmonic maps, analogous…

We introduce the notion of Canonical Expanding Ricci Soliton, and use it to derive new Harnack inequalities for Ricci flow. This viewpoint also gives geometric insight into the existing Harnack inequalities of Hamilton and Brendle.

This paper studies the Ricci flow on closed manifolds admitting harmonic spinors. It is shown that Perelman's Ricci flow entropy can be expressed in terms of the energy of harmonic spinors in all dimensions, and in four dimensions, in terms…

We describe three-dimensional Lorentzian homogeneous Ricci solitons, showing that all types (i.e. shrinking, expanding and steady) exist. Moreover, all non-trivial examples have non-diagonalizable Ricci operator with one only eigenvalue.

In this paper we consider connections between Ricci solitons and Einstein metrics on homogeneous spaces. We show that a semi-algebraic Ricci soliton admits an Einstein one-dimensional extension if the soliton derivation can be chosen to be…

We decribe and announce some results (joint with G. Besson, L. Bessieres, M. Boileau and J.Porti) about the geometry and topology of 3-manifolds. Most of the article is primarily intended as an introduction for nonexperts to geometrization…

We consider gradient Ricci solitons conformal to a $n$-dimensional pseudo-Euclidean space and we completely describe the most general ansatz that reduces the resulting system of partial differential equations to a system of ordinary…

It is known that all left-invariant pseudo-Riemannian metrics on $H_3$ are algebraic Ricci solitons. We consider generalizations of Riemannian $H$-type, namely pseudo$H$-type and $pH$-type. We study algebraic Ricci solitons of…

The aim of the present survey paper is to provide an accessible introduction to a new chapter of representation theory - harmonic analysis for noncommutative groups with infinite-dimensional dual space. I omitted detailed proofs but tried…

The aim of this article is to explore the Clairaut anti-invariant Riemannian maps from/to K\"ahler manifolds admitting Ricci solitons. We find the curvature relations and calculate the Ricci tensor under different conditions. We discuss the…

In this paper we investigate the space of harmonic maps from a 2-torus to $\mathbb{S}^3$ using the spectral curve correspondence and Whitham deformations. In an open and dense subset of a parameter space we find that the space of harmonic…

We present a monotonic expression for the Ricci flow, valid in all dimensions and without curvature assumptions. It is interpreted as an entropy for a certain canonical ensemble. Several geometric applications are given. In particular, (1)…

$\infty$-Harmonic maps are a generalization of $\infty$-harmonic functions. They can be viewed as the limiting cases of p-harmonic maps as p goes to infinity. In this paper, we give complete classifications of linear and quadratic…

Non-polynomial growth harmonic maps from the complex plane to the hyperbolic space are studied. Some non-surjectivity results are obtained. Moreover, images of such harmonic maps are investigated with reference to their Hopf differentials.

In this paper we study the global behavior of the Ricci flow equation for two classes of homogeneous manifolds with two isotropy summands. Using methods of the qualitative theory of differential equations, we present the global phase…

We extend Grood's tableau construction of irreducible representations of the rook monoid and Steinberg's analogous result for the full transformation monoid. Our approach is characteristic-free and applies to any submonoid $\mathcal{M}(n)$…

Lie derivatives of various geometrical and physical quantities define symmetries and conformal symmetries in general relativity. Thus we obtain motions, collineations, conformal motions and conformal collineations. These symmetries are used…