arXiv research

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 homogeneous (and also invariant) pseudo-Riemannian Ricci solitons which are not isom…

New non-trivial Kaehler-Ricci solitons found in infinite dimensional complex space forms.

Characterizes G2-structures on Lie algebras with non-trivial center.

This paper classifies Kähler manifolds with specific Einstein-type properties.

The paper explores Kähler-Ricci solitons with maximal symmetry in complex dimension two.

The aim of this note is to prove that any compact non-trivial almost Ricci soliton $\big(M^n,\,g,\,X,\,λ\big)$ with constant scalar curvature is isometric to a Euclidean sphere $\Bbb{S}^{n}$. As a consequence we obtain that every compact non-trivial almost Ricci soliton with constant scalar curvature is gradient. Moreo…

Study on shrinking solitons of generalized Ricci flow.

We prove the following results: (i) A Sasakian metric as a non-trivial Ricci soliton is null $η$-Einstein, and expanding. Such a characterization permits to identify the Sasakian metric on the Heisenberg group $\mathcal{H}^{2n+1}$ as an explicit example of (non-trivial) Ricci soliton of such type. (ii) If an $η$-Einste…

We study gradient Ricci solitons with maximal symmetry. First we show that there are no non-trivial homogeneous gradient Ricci solitons. Thus the most symmetry one can expect is an isometric cohomogeneity one group action. Many examples of cohomogeneity one gradient solitons have been constructed. However, we apply the…

Study on LP-Sasakian manifolds with generalized η-Ricci solitons.

New examples of Kähler-Ricci solitons on Fano threefolds with non-trivial moduli found.

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.

Study on dimensions of Killing vector fields on gradient Ricci solitons.

Study on gradient solitons on specific manifolds.

Non-trivial obstructions found for topological solitons in Yang-Mills-Chern-Simons theories.

The paper studies integral formulas for a specific type of soliton.

The article characterizes gradient ρ-Einstein solitons under specific conditions.

The study characterizes quasi Yamabe solitons with potential vector fields.

The main purpose of the paper is to prove that if a compact Riemannian manifold admits a gradient $ρ$-Einstein soliton such that the gradient Einstein potential is a non-trivial conformal vector field, then the manifold is isometric to the Euclidean sphere. We have showed that a Riemannian manifold satisfying gradient …

Researchers find limits on curvature of certain 3D solitons.

Study on gradient pseudo-Ricci solitons on real hypersurfaces.

Symphonic maps on non-compact Riemannian manifolds are non-existent.

The study characterizes spacetimes with specific solitons in $f(\mathcal{R})$-gravity.

Study of ends of complete gradient Schouten solitons, showing finitely many ends for shrinking and connected infinity for expanding ones.

Defines and studies Clairaut Riemannian maps between manifolds and Ricci solitons.

Study on solitons in specific geometric manifolds, proving manifold properties and presenting examples.

The study finds Ricci solitons on a specific type of 3D Lorentzian Walker manifold.

The paper defines Hesse solitons and explores their properties on Hessian manifolds.

Study shows Kähler gradient Ricci solitons have limited symmetry groups.

Using certain solutions of the curve shortening flow, including self-shrinking and self-expanding curves or spirals, we construct and characterize many new examples of translating solitons for mean curvature flow in complex Euclidean plane. They generalize the Joyce, Lee and Tsui ones \cite{JLT} in dimension two. The s…

We consider the non-trivial Ricci soliton on $\mathbb{CP}^2\#\overline{\mathbb{CP}^2}$ constructed by Koiso and Cao. It is a Kähler metric invariant by the $U(2)$ action on $\mathbb{CP}^2\#\overline{\mathbb{CP}^2}$. We study its Yamabe equation and prove it has exactly one $U(2)-$invariant solution up to homothecies.

This paper studies cohomogeneity one Ricci solitons. If the isotropy representation of the principal orbit $G/K$ consists of two inequivalent $Ad_K$-invariant irreducible summands, the existence of parameter families of non-homothetic complete steady and expanding Ricci solitons on non-trivial bundles is shown. These e…

Study of almost Yamabe solitons on Kaehler submersions.

We consider Fano manifolds admitting an algebraic torus action with general orbit of codimension one. Using a recent result of Datar and Szekelyhidi, we effectively determine the existence of Kahler-Ricci solitons for those manifolds via the notion of equivariant K-stability. This allows us to give new examples of Kahl…

We introduce a class of overdetermined systems of partial differential equations of finite type on (pseudo)-Riemannian manifolds that we call the generalised Ricci soliton equations. These equations depend on three real parameters. For special values of the parameters they specialise to various important classes of equ…

We show that a Born-Infeld soliton can be realised either as a spacelike minimal graph or timelike minimal graph over a timelike plane or a combination of both away from singular points. We also obtain some exact solutions of the Born-Infeld equation from already known solutions to the maximal surface equation. Further…

The paper characterizes Clairaut conformal submersions on Ricci solitons.

The paper explores conformal submersions from Ricci solitons to Riemannian manifolds.

The paper studies Riemannian maps with Ricci soliton base manifolds.

New method constructs nilpotent Lie algebras from quivers.

Study Clairaut maps on Kähler manifolds with Ricci solitons, finding curvature and scalar relations.

This paper studies Kähler-Ricci solitons on Heisenberg groups and related metrics.

The study explores δ-almost gradient Yamabe solitons on pseudo-Riemannian manifolds.

The study investigates properties of a specific Riemannian manifold with a semi-symmetric non-metric connection.

In this paper we establish the existence of extremals for the Log Sobolev functional on complete non-compact manifolds with Ricci curvature bounded from below and strictly positive injectivity radius, under a condition near infinity. When Ricci curvature is also bounded from above we get exponential decay at infinity o…

In this paper, we first show an interpretation of the Kähler-Ricci flow on a manifold $X$ as an exact elliptic equation of Einstein type on a manifold $M$ of which $X$ is one of the (Kähler) symplectic reductions via a (non-trivial) torus action. There are plenty of such manifolds (e.g. any line bundle on $X$ will do).…

A Euclidean minimal torus with planar ends gives rise to an immersed Willmore torus in the conformal 3--sphere $S^3=\R^3\cup \{\infty\}$. The class of Willmore tori obtained this way is given a spectral theoretic characterization as the class of Willmore tori with reducible spectral curve. A spectral curve of this type…

Develops a new framework for generalized Ricci flow on Lie groups.