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http://dx.doi.org/10.4134/JKMS.j190201

GRADIENT ALMOST RICCI SOLITONS WITH VANISHING CONDITIONS ON WEYL TENSOR AND BACH TENSOR  

Co, Jinseok (Department of Mathematics Chung-Ang University)
Hwang, Seungsu (Department of Mathematics Chung-Ang University)
Publication Information
Journal of the Korean Mathematical Society / v.57, no.2, 2020 , pp. 539-552 More about this Journal
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;
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