Algebraic Ricci solitons in the Finslerian case
Bull. Korean Math. Soc. 2021 Vol. 58, No. 4, 853-863
Published online February 26, 2021
Printed July 31, 2021
Guocheng Jiao, Zaili Yan
Ningbo University; Ningbo University
Abstract : In this paper, we study algebraic Ricci solitons in the Finslerian case. We show that any simply connected Finslerian algebraic Ricci soliton is a Finslerian Ricci soliton. Furthermore, we study Randers algebraic Ricci solitons. It turns out that a shrinking, steady, or expanding Randers algebraic Ricci soliton with vanishing S-curvature is Einstein, locally Minkowskian, or Riemannian, respectively.
Keywords : Homogeneous Finsler space, Ricci soliton, Finslerian algebraic Ricci soliton
MSC numbers : Primary 53C60, 53C30, 53C25
Supported by : This work was financially supported by NSFC 11701300 and K. C. Wong Magna Fund in Ningbo University.
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