arXiv research

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

Study on Ricci-Bourguignon solitons on specific product spaces.

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

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 examines triviality of Ricci-Bourguignon harmonic solitons.

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

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

Study clarifies almost Ricci-Bourguignon solitons and their properties.

Sharp inequalities and solitons studied in statistical submersions.

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

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

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

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

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

New examples of solitons found as warped products.

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…

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

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

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…

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.

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

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 $…

In this work we generalise various recent results on the evolution and monotonicity of the eigenvalues of certain geometric operators under specified geometric flows. Given a closed, compact Riemannian manifold $\big(M^n,g(t)\big)$ and a smooth function $η\in C^{\infty}(M)$ we consider the family of operators $\mathbb{…