Gradient almost Ricci solitons with vanishing conditions on Weyl tensor and Bach tensor.
J. Korean Math. Soc.
Published online July 17, 2019
Jinseok Co and Seungsu Hwang
Chungang university
Abstract : In this paper we consider gradient almost Ricci solitons with weak conditions on
Weyl and Bach tensors. We show that a gradient almost Ricci soliton has harmonic Weyl
curvature if it has fourth order divergence-free Weyl tensor, or it has divergence-free Bach tensor.
Furthermore, if its Weyl tensor is radially flat, we prove such a gradient almost Ricci soliton is
locally a warped product with Einstein fibers. Finally, we prove a rigidity result on compact
gradient almost Ricci solitons satisfying an integral condition.
Keywords : gradient almost Ricci soliton, harmonic Weyl curvature, conformally flat.
MSC numbers : 53C25
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