arXiv research

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 characterizes $\ast$-Ricci-Bourguignon solitons on Kenmotsu manifolds.

The paper examines triviality of Ricci-Bourguignon harmonic solitons.

Study on Ricci-Bourguignon solitons on specific product spaces.

Study on mixed Killing vector fields on Cigar Ricci-Bourguignon solitons.

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

The paper studies a new soliton on Kenmotsu manifolds and derives its scalar curvature.

Study clarifies almost Ricci-Bourguignon solitons and their properties.

New examples of solitons found as warped products.

Sharp inequalities and solitons studied in statistical submersions.

The study explores rigid constraints on almost Ricci-Bourguignon solitons on contact metric three-manifolds.

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

Study vector fields on hyperbolic spaces to create Ricci-Bourguignon solitons.

The study characterizes mixed super quasi-Einstein manifolds with Ricci-Bourguignon solitons.

Study geometric and analytical properties of $ρ$-Einstein solitons.

In this paper we present some results on a family of geometric flows introduced by Bourguignon that generalize the Ricci flow. For suitable values of the scalar parameter involved in these flows, we prove short time existence and provide curvature estimates. We also state some results on the associated solitons.

In this paper the notion of Ricci $ρ$-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 $M$ be a $ρ$-soliton, then $M$ is a Kenmotsu manifold of constant sectional curvature $…

New solitons defined for Sasaki-like almost contact complex Riemannian manifolds.

Existence of non-Einstein, non-shrinking Ricci solitons on quaternionic and octonionic spaces.

In this paper we consider a perturbation of the Ricci solitons equation proposed by J. P. Bourguignon in \cite{jpb1}. We show that these structures are more rigid then standard Ricci solitons. In particular, we prove that there is only one complete three--dimensional, positively curved, Riemannian manifold satisfying $…

Gradient estimates for a parabolic PDE under Ricci-Bourguignon flow on warped product manifolds.

The paper proves estimates for a specific flow on compact manifolds.

In this paper, we study the Ricci-Bourguignon flow on higher dimensional classical Heisenberg nilpotent Lie groups and construct a solution of this flow on Heisenberg and quaternion nilpotent Lie groups. In the end, we investigate the deformation of spectrum and length spectrum on compact nilmanifolds obtained of Heise…

Let $M$ be an $n$-dimensional closed Riemannian manifold with metric $g$, $dμ=e^{-φ(x)}dν$ be the weighted measure and $Δ_{p,φ}$ be the weighted $p$-Laplacian. In this article we will investigate monotonicity for the first eigenvalue problem of the weighted $p$-Laplace operator acting on the space of functions along th…

In this paper, we study monotonicity of eigenvalues of Laplacian-type operator $-Δ+cR$, where $c$ is a constant, along the Ricci-Bourguignon flow. For $c\neq0$, We derive monotonicity of the lowest eigenvalue of Laplacian-type operator $-Δ+cR$ which generalizes some results of Cao \cite{Cao2007}. For $c=0$, We derive m…

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.

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.

Extended solitons show constant curvature on compact manifolds.

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…

3D solitons classified into specific types.