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Information Journal Paper

Title

On projectively related Finsler gradient Ricci solitons

Pages

  30-47

Abstract

 In this paper, we study pointwise projectively related Finsler gradient Ricci solitons. We obtain an equation that characterizes the relationship between two pointwise projectively related Finsler gradient Ricci solitons. Further, if two Finsler gradient Ricci solitons (M, F, dV ˜ F˜) and (M, F, dVF ) satisfy F˜,k = µ ∂[F˜2 ] ∂yk and some extra conditions, where “, ” denotes the horizontal covariant derivative with respect to F, we characterize their relationships along the geodesics. In particular, if two Finsler gradient Ricci solitons are both complete, then (M, F, dVF ) is expanding or shrinking and (M, F, dV ˜ F˜) is shrinking.

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