Journal
PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY
Volume -, Issue -, Pages -Publisher
AMER MATHEMATICAL SOC
DOI: 10.1090/proc/16240
Keywords
Finsler gradient Ricci soliton; weighted Ricci curvature; Randers measure space; Finsler Gaussian shrinking soliton; S-curvature
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In this paper, the authors study a class of Finsler measure spaces whose weighted Ricci curvature satisfies Ric infinity = cF2. This class includes all gradient Ricci solitons and Finsler Gaussian shrinking solitons. Therefore, Finsler measure spaces in this class are called Finsler gradient Ricci solitons. The authors also find sufficient and necessary conditions for a Randers measure space to be a Finsler gradient Ricci soliton and prove that Randers-Finsler gradient Ricci solitons must have isotropic S-curvature. They also provide an equivalent condition for a Randers measure space to be a Finsler gradient Ricci soliton of constant S-curvature.
In this paper, we study a class of Finsler measure spaces whose weighted Ricci curvature satisfies Ric infinity = cF2. This class contains all gradient Ricci solitons and Finsler Gaussian shrinking solitons. Thus Finsler measure spaces in this class are called Finsler gradient Ricci solitons. For a Randers measure space, we find sufficient and necessary conditions for this space to be a Finsler gradient Ricci soliton. In particular, we show that Randers-Finsler gradient Ricci solitons must have isotropic S-curvature. Finally, we give an equivalent condition for a Randers measure space to be a Finsler gradient Ricci soliton of constant S-curvature.
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