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arXiv · 1604.04087

Bach-flat h-almost gradient Ricci solitons

Gabjin Yun·Jinseok Co·Seungsu Hwang
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Abstract

On an $n$-dimensional complete manifold $M$, consider an $h$-almost gradient Ricci soliton, which is a generalization of a gradient Ricci soliton. We prove that if the manifold is Bach-flat and $dh/du>0$, then the manifold $M$ is either Einstein or rigid. In particular, such a manifold has harmonic Weyl curvature. Moreover, if the dimension of $M$ is four, the metric $g$ is conformally flat.

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Gabjin Yun, Jinseok Co, Seungsu Hwang. 2016-04-14. Bach-flat h-almost gradient Ricci solitons. https://doi.org/10.2140/pjm.2017.288.475

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