Einstein warped-product manifolds and the screened Poisson equation

TL;DR

This paper investigates Einstein warped-product manifolds where the warping function satisfies a homogeneous screened Poisson equation, revealing relationships between manifold dimension, Ricci curvature, and the screened parameter.

Contribution

It establishes a novel connection between Einstein warped-product manifolds and the homogeneous screened Poisson equation, deriving a quadratic relation among key geometric parameters.

Findings

Dimension, Ricci curvature, and screened parameter are related through a quadratic equation.

The study characterizes conditions under which the warping function satisfies the homogeneous screened Poisson equation.

Provides new insights into the structure of Einstein warped-product manifolds with specific PDE constraints.

Abstract

We study a particular type of Einstein warped-product manifold where the warping function must satisfy the homogeneous version of the screened Poisson equation. Under these assumptions, we show that the dimension of the manifold, the (constant negative) Ricci curvature and the screened parameter are related through a quadratic equation.