J. Korean Math. Soc. 2020; 57(2): 539-552
Online first article July 17, 2019 Printed March 1, 2020
https://doi.org/10.4134/JKMS.j190201
Copyright © The Korean Mathematical Society.
Jinseok Co, Seungsu Hwang
Chung-Ang University; Chung-Ang University
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: Primary 53C25; Secondary 58E11
Supported by: The second author was supported by the National Research Foundation of Korea (NRF-2018R1D1A1B05042186).
2019; 56(2): 329-352
2009; 46(3): 449-461
2011; 48(4): 669-689
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