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arXiv · 2505.18834

On quasi-Einstein manifolds with constant scalar curvature

Johnatan Costa·Ernani Ribeiro Jr·Márcio Santos
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Abstract

In this article, we study quasi-Einstein manifolds with constant scalar curvature. We provide a classification of compact and noncompact (possibly with boundary) $T$-flat quasi-Einstein manifolds with constant scalar curvature, where the $T$-tensor is directly related to the Cotton and Weyl tensors. Moreover, we construct new explicit examples of noncompact quasi-Einstein manifolds. In addition, we prove a complete classification of compact and noncompact (possibly with boundary) $3$-dimensional $m$-quasi-Einstein manifolds with constant scalar curvature.

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Johnatan Costa, Ernani Ribeiro Jr, Márcio Santos. 2025-05-24. On quasi-Einstein manifolds with constant scalar curvature. https://arxiv.org/abs/2505.18834

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