A note on gradient Einstein-type manifolds
Differential Geometry
2021-05-04 v2
Abstract
In this note, we show that a nontrivial, compact, degenerate or nondegenerate, gradient Einstein-type manifold of constant scalar curvature is isometric to the standard sphere with a well defined potential function. Moreover, under some geometric assumptions, the noncompact case is also treated. In this case, the main result is that a homogeneous, proper, noncompact, nondegenerate, gradient Einstein-type manifold is an Einstein manifold.
Keywords
Cite
@article{arxiv.1710.10549,
title = {A note on gradient Einstein-type manifolds},
author = {José Nazareno Vieira Gomes},
journal= {arXiv preprint arXiv:1710.10549},
year = {2021}
}
Comments
Final version which has been accepted for publication in Differential Geometry and its Applications