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arXiv · 1907.11952

An analysis of symmetry groups of generalized $m$-quasi-Einstein manifolds

Paula Correia·Benedito Leandro·Romildo Pina
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Abstract

In this paper emphasis is placed on how the behavior of the solutions of a PDE is affected by the geometry of the generalized $m$-quasi-Einstein manifold, and vice versa. Considering a $n$-dimensional generalized $m$-quasi-Einstein manifold which is conformal to a pseudo-Euclidean space, we prove the most general symmetry group of maximal dimension. Moreover, we demonstrate that there is no different 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 shrinking $m$-quasi-Einstein manifold (cf. Example 3). A discussion about the fluid ball conjecture was made.

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Paula Correia, Benedito Leandro, Romildo Pina. 2019-07-27. An analysis of symmetry groups of generalized $m$-quasi-Einstein manifolds. https://arxiv.org/abs/1907.11952

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