An analysis of symmetry groups of generalized $m$-quasi-Einstein manifolds
Volume 173 / 2023
Colloquium Mathematicum 173 (2023), 77-88
MSC: Primary 53C18; Secondary 53C20, 53C21, 53C25.
DOI: 10.4064/cm8811-2-2023
Published online: 3 April 2023
Abstract
In this paper, emphasis is placed on how the behavior of the solutions of a system of PDEs is affected by the geometry of generalized $m$-quasi-Einstein manifold, and vice versa. Considering an $n$-dimensional generalized $m$-quasi-Einstein manifold which is conformal to a pseudo-Euclidean space, we find the most general symmetry group of maximal dimension. Moreover, we demonstrate that there is no other low-dimensional invariant on a generalized $m$-quasi-Einstein manifold. As an application, we use the invariant structure of the metric to provide an example of a shrinking $m$-quasi-Einstein manifold.
