arXiv research

Study properties of para-Kähler manifolds with conformal Einstein soliton metrics.

The paper studies Ricci curvature on Kähler-Ricci flow.

Let $M^n$ be a compact K$\ddot{a}$hler manifold with almost nonnegative Ricci curvature and nonzero first Betti number. We show that the holomorphic Euler number of $M^n$ vanishes, which gives a new obstruction for compact complex manifolds admitting K$\ddot{a}$hler metrics with almost nonnegative Ricci curvature. A cr…

We develop a parabolic pluripotential theory on compact K{ä}hler manifolds, defining and studying weak solutions to degenerate parabolic complex Monge-Amp{è}re equations. We provide a parabolic analogue of the celebrated Bedford-Taylor theory and apply it to the study of the K{ä}hler-Ricci flow on varieties with log te…

We establish a stability result for elliptic and parabolic complex Monge-Amp{è}re equations on compact K{ä}hler manifolds, which applies in particular to the K{ä}hler-Ricci flow. Dedicated to Jean-Pierre Demailly on the occasion of his 60th birthday.

In this paper we prove that for a complete, connected and oriented Käler affine manifold $(M,G)$ of dimension $n,$ if it is Kähler affine Ricci flat or the K$\ddot{a}$hler affine scalar curvature $S\equiv0,$ ($n\leq 5$), then the universal covering manifold $\widetilde{M}$ of $M$ is isometric to the Euclidean n-space $…

For any complete noncompact K$\ddot{a}$hler manifold with nonnegative and bounded holomorphic bisectional curvature,we provide the necessary and sufficient condition for non-ancient solution to the Ricci flow in this paper.

By establishing two general quadratic inequalities, we obtain some inequalities related to Ricci curvatures for Lagrangian submanifolds of K$\ddot{\mathrm{a}}$hler QCH-manifolds, which generalize some results for Lagrangian submanifolds of complex space forms.

Study complex Monge-Ampère flows on Kähler manifolds using Perron method.

Study on shrinking solitons of generalized Ricci flow.

We classify Algebraic Ricci Solitons of three-dimensional Lorentzian Lie groups. All algebraic Ricci solitons that we obtain are sol-solitons. In particular, we prove that, contrary to the Riemannian case, Lorentzian Ricci solitons need not to be algebraic Ricci solitons. We classify Algebraic Ricci Solitons of three-d…

Study on $η$-Ricci-Yamabe solitons on Riemannian submersions.

Study on geometric properties of second Ricci solitons.

New examples of solitons found as warped products.

We prove some results for the solitons of the Ricci-Bourguignon flow, generalizing corresponding results for Ricci solitons. Taking motivation from Ricci almost solitons, we then introduce the notion of Ricci-Bourguignon $almost$ solitons and prove some results about them which generalize previous results for Ricci alm…

The paper explores almost Ricci solitons on Finsler spaces, proving conditions for their existence.

Survey paper analyzes curvature estimates for 4D gradient Ricci solitons.

The study classifies h-almost Ricci-Yamabe solitons in various paracontact manifolds.

The study classifies steady Ricci solitons based on geometric conditions.

The paper characterizes Ricci solitons on the Poincaré upper half plane.

The paper examines triviality of Ricci-Bourguignon harmonic solitons.

Study characterizes Einstein manifolds in almost Ricci solitons.

This paper provides a study of algebraic Ricci solitons in the pseudo-Riemannian case. In the Riemannian case, all nontrivial homogeneous algebraic Ricci solitons are expanding algebraic Ricci solitons. In this paper, we obtain a steady algebraic Ricci soliton and a shrinking algebraic Ricci soliton in the Lorentzian s…

The study proves triviality and rigidity results for Ricci solitons and estimates their conjugate radius.

Study on transverse Ricci solitons on compact foliated manifolds.

Study on Ricci-like solitons and gradient solitons on specific manifolds.

Study on pseudo-Riemannian algebraic Ricci solitons in 4D Lie groups.

Study of $η$-Ricci solitons on Kenmotsu 3-manifolds.

New curvature condition proves rigidity of Bryant Ricci solitons.

Paper proves rigidity for Ricci solitons with specific conditions.

We introduce the concept {\it $h$-almost Ricci soliton} which extends naturally the {\it almost Ricci soliton} by Pigola-Rigoli-Rimoldi-Setti and show that a compact nontrivial $h$-almost Ricci soliton of dimension no less than three with $h$ having defined signal and constant scalar curvature is isometric to a standar…

Characterizes $*$-$k$-Ricci-Yamabe solitons on Kenmotsu manifolds.

Study 4D steady gradient Ricci solitons reducing to 3D manifolds.

In this paper, we consider $*$-Ricci soliton in the frame-work of Kenmotsu manifolds. First, we prove that if the metric of a Kenmotsu manifold $M$ is a $*$-Ricci soliton, then soliton constant $λ$ is zero. For 3-dimensional case, if $M$ admits a $*$-Ricci soliton, then we show that $M$ is of constant sectional curvatu…

We introduce a flow of Kähler structures over Fano manifolds with formal limit at infinite time a Kähler-Ricci soliton. This flow correspond to a Perelman's modified backward Kähler-Ricci type flow that we call Soliton-Kähler-Ricci flow. It can be generated by the Soliton-Ricci flow. We assume that the Soliton-Ricci fl…

The paper characterizes solitons and estimates scalar curvature.

The paper examines conditions for conformal Ricci solitons on generalized ($κ, μ$)-space forms.

Study on p-biharmonic maps from gradient Ricci solitons, focusing on 2D cigar soliton.

New classification of gradient steady Ricci solitons with vanishing D-tensor.

Defines a new metric on Fano Kaehler-Ricci solitons.

The paper examines Sasaki-Ricci solitons and their transverse rigidity properties.

The paper investigates geometrical aspects of static spacetime with almost gradient Ricci solitons.

New expanding Ricci solitons found starting in dimension four.

The paper studies conformal Ricci solitons in warped product spaces.

Study on para-Sasakian metrics and their solitons.

Hyperbolic solitons on trans-Sasakian space forms and their submanifolds

In this paper, we study Riemannian submersions whose total manifolds admitting a Ricci soliton. Here, we characterize any fiber of such a submersion is Ricci soliton or almost Ricci soliton. Indeed, we obtain necessary conditions for which the target manifold of Riemannian submersion is a Ricci soliton. Moreover, we st…

Paper classifies 3D breathers and generalizes Ricci soliton results.