Sobre variedades quasi-Einstein generalizadas

Abstract

This work aims to explain a stiffness result for a class of generalized quasi-Einstein compact manifolds with constant scalar curvature. Furthermore, under some geometric assumptions, the stiffness for the non-compact case is also proved. Considering nonconstant scalar curvature, we characterize and present two classes of complete generalized quasi-Einstein manifolds conforming to Euclidean space that are obtained by taking potential functions and conforming factors as radial or invariant under the action of a translation group (n-1)-dimensional (see Freitas Filho, A. A. and Tenenblat, K. [On generalized quasi-Einstein manifolds, J. Geom. Phys. 178 (2022) 104562]).