A note on gradient Einstein-type manifolds
arXiv:1710.10549 · doi:10.1016/j.difgeo.2019.04.002
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.
Final version which has been accepted for publication in Differential Geometry and its Applications