对偶平坦的Kropina度量的共形性质
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摘要
研究了对偶平坦的Kropina度量的共形性质,利用对偶平坦、共形相关与其测地系数之间的关系,证明了对偶平坦和共形平坦的Kropina度量是闵可夫斯基度量,并得到了两个对偶平坦的Kropina度量之间的共形变换必然是位似变换.
In this paper,the conformal properties of dual flat Kropina metrics are studied.Using the relations among dual flat,conformally related and geodesic coefficients of kropina metrics,it is proved that dual flat and conformally flat Kropina metrics are Minkowskian.Further,the conformal transformation between two dual flat kropina metrics must be homothetic.
In this paper,the conformal properties of dual flat Kropina metrics are studied.Using the relations among dual flat,conformally related and geodesic coefficients of kropina metrics,it is proved that dual flat and conformally flat Kropina metrics are Minkowskian.Further,the conformal transformation between two dual flat kropina metrics must be homothetic.
引文
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[2]BACSO S,CHENG X.Finsler conformal transformalations and the curcature invariances[J].Publ Math Debrecen,2007,70:221-231.
[3]AMARI S,NAGAOKA H.Methods of information geometry[M].Oxford:Oxford University Press,2000.
[4]SHEN Z M.Riemann-finsler geometry with applications to information geometry[J].Chin Ann Math Ser B,2006,27(1):73-94.
[5]XIA Q L.On locally dually flat(α,β)-metrics[J].Differential Geometry and Its Applications,2011,29(2):233-243.
[6]CHEN G Z,LIU L H.On dually flat Kropina metrics[J].International Journal of Mathematics,2016,27(12):1-13.
[7]KROPINA V K.On projective two-dimensional Finsler spaces with a special metric[J].Trudy Sem Vektor Tenzor Anal,1961,11:277-292.
[8]ANTONELLI P L,INGARDEN R S,MATSUMOTO M.The theory of sprays and Finsler spaces with applications in physics and biology[M].New York:Springer,1993.