1,720,971 research outputs found
Ricci-Bourguignon flow on an open surface
No full textIn this paper, we investigate the normalized Ricci-Bourguignon flow with incomplete initial metric on an open surface. We show that such a flow converges exponentially to a metric with constant Gaussian curvature if the initial metric is suitable. In particular, if the initial metric is complete then the metrics converge to the standard hyperbolic metric
New solutions to Einstein's equations to find Walker manifolds
Full text linkIn this paper, we investigate the Einsteinian manifolds with parallel null distribution. For this, we first obtain the equations that lead to finding the mentioned manifolds. These equations are known as Einstein's equations. Then we reduce these equations by using Lie symmetry method. These equations are known as Einstein's equations. In this method, we first obtain the generators of the symmetry algebra and then calculate the differential invariants for each of the generators and calculate the group invariant solutions of this equation. In addition to this, we also obtain the optimal system of the one-dimensional sub-algebras of these equations. This optimal system helps us to have a classification on group invariant solutions using conjugate mapping
EIGENVALUES VARIATION OF THE P-LAPLACIAN UNDER THE RICCI FLOW ON SM
No full textLet (M,F) be a compact Finsler manifold. Studying the eigenvalues and eigenfunctions for the linear and nonlinear geometric operators is a known problem. In this paper we will consider the eigenvalue problem for the p-laplace operator for Sasakian metric acting on the space of functions on SM. We find the first variation formula for the eigenvalues of p-Laplacian on SM evolving by the Ricci flow on M and give some examples.DOI : http://dx.doi.org/10.22342/jims.22.2.215.157-177</jats:p
Harmonic-hyperbolic geometric flow
No full textIn this article we study a coupled system for hyperbolic geometric
flow on a closed manifold M, with a harmonic flow map from M to
some closed target manifold N.
Then we show that this flow has a unique solution for a short-time.
After that, we find evolution equations for Riemannian curvature tensor,
Ricci curvature tensor, and scalar curvature of M under this flow.
In the final section we give some examples of this flow on closed manifolds
Gradient estimate of a Poisson equation under the almost Ricci solitons
No full textAbstract In this paper, we consider an n-dimensional manifold M n endowed with an almost Bakry–Émery Ricci curvature and study a special case of gradient estimate for the positive solutions of Δ u − X . u = f , for a smooth function f and a smooth vector field X under the almost Ricci solitons condition
Some Results of Ricci Bi-Conformal Vector Fields
Full text linkThe investigation of Ricci bi-conformal vector fields and their associated outcomes is crucial for gaining insights into the geometric and topological characteristics of the underlying manifolds. The study of conformal vector fields and their extensions is highly valuable in the realms of geometry and physics. In this manuscript, we study the topological properties of the Ricci bi-conformal vector field. The goal of this paper is to find some results of the Ricci bi-conformal vector fields. We prove that a complete manifold admits the Ricci bi-conformal vector fields has a finite fundamental group. For this purpose, we first state the definition and lemma, and then use them to prove our theorems
Gradient Ricci Bourguignon solitons on perfect fluid space-times
Full text linkThe main purpose of the present paper is about characterizing the properties of the perfect fluid space-time that admits the gradient Ricci-Bourguignon soliton. This gives some results about the stability of the energy-momentum tensor and also under some conditions pursues that a perfect fluid space-time is Ricci symmetric. As a special case, when a perfect fluid space-time is equipped with the Ricci-Bourguignon soliton which has Ricci biconformal vector field, we show that the metric of this space is Einstein
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