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arXiv · 1710.10549

A note on gradient Einstein-type manifolds

José Nazareno Vieira Gomes
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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.

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José Nazareno Vieira Gomes. 2017-10-29. A note on gradient Einstein-type manifolds. https://doi.org/10.1016/j.difgeo.2019.04.002

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