On quasi-Einstein manifolds with constant scalar curvature

TL;DR

This paper classifies and constructs examples of quasi-Einstein manifolds with constant scalar curvature, focusing on compact and noncompact cases, and provides a complete classification in three dimensions.

Contribution

It offers a comprehensive classification of $T$-flat quasi-Einstein manifolds with constant scalar curvature, including new explicit examples and a complete 3D classification.

Findings

Classification of compact and noncompact $T$-flat quasi-Einstein manifolds

Construction of new explicit noncompact examples

Complete classification of 3D $m$-quasi-Einstein manifolds

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.