关于共形Berwald的Kropina度量(英文)
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摘要
本文利用导航数据研究了共形Berwald的Kropina度量.首先利用导航数据刻画了Berwald Kropina度量.在此基础上,本文得到了Kropina度量是共形Berwald度量的一个充分必要条件.进一步,刻画了具有弱迷向旗曲率的共形Berwald Kropina度量的局部结构.
In this paper,we study the conformally Berwald Kropina metrics via navigation data.We first characterize Berwald Kropina metrics via navigation data.Based on this,we obtain a sufficient and necessary conditions that a Kropina metric is conformally Berwald metric.Further,we characterize the local structure of conformally Berwald Kropina metrics of weakly isotropic flag curvature.
In this paper,we study the conformally Berwald Kropina metrics via navigation data.We first characterize Berwald Kropina metrics via navigation data.Based on this,we obtain a sufficient and necessary conditions that a Kropina metric is conformally Berwald metric.Further,we characterize the local structure of conformally Berwald Kropina metrics of weakly isotropic flag curvature.
引文
[1]Bacso,S.and Cheng,X.Y.,Pinsler conformal transformations and the curvature invariances,Publ.Math.Debrecen,2007,70(1/2):221-231.
[2]Bacso,S.,Cheng,X.Y.and Shen,Z.M.,Curvature properties of(α,β)-metrics,Adv.Stud.Pure Math.,2007,48:73-110.
[3]Chen,G.Z.,Cheng,X.Y.,An important class of conformally flat weak Einstein Finsler metrics,Internat.J.Math.,2013,24(1):Article ID 1350003,15 pages.
[4]Cheng,X.Y.and Shen,Z.M.,Finsler Geometry—An Approach via Randers Spaces,Beijing:Science Press,2012.
[5]Chern,S.S.and Shen,Z.M.,Rieman-Finsler Geometry,Nankai Tracts Math.,Vol.6,Singapore:World Scientific,2005.
[6]Ingarden,R.S.,Geometry of thermodynamics,Diff.Geom.Methods in Theor.Phys.(Doebner,H.D.et al.eds.),XV Intern.Conf.Clausthal,1986,Singapore:World Scientific,1987.
[7]Hojo,S.,Matsumoto,M.and Okubo,K.,Theory of conformally Berwald Finsler spaces and its applications to(α,β)-metrics,Balkan J.Geom.Appl,2000,5(1):107-118.
[8]Kropina,V.K.,On projective Finsler spaces with a certain special form,Naucn.Doklady Vyss.Skoly,Fiz.-Mat.Nauki,1959,2:38-42(in Russian).
[9]Kropina,V.K.,On projective two-dimensional Finsler spaces with a special metric,Trudy Sem.Vektor.Tenzor.Anal.,1961,11:277-292.
[10]Matsumoto,M.and Hojo,S.,A conclusive theorem on C-reducible Finsler spaces,Tensor(N.S.),1978,32:225-230.
[11]Matsumoto,M.,Finsler spaces of constant curvature with Kropina metric,Tensor(N.S.),1991,50:194-201.
[12]Matsumoto,M.,The Berwald connections of a Finsler spaces with(α,β)-metric,Tensor(N.S.),1991,50:18-21.
[13]Shibata,C,On Finsler spaces with Kropina metric,Rep.Math.Phys.,1978,13:117-128.
[14]Xia,Q.L.,On Kropina metrics of scalar flag curvature,Differential Geom.Appl,2013,31:393-404.
[15]Yoshikawa,R.and Okubo,K.,Kropina spaces of constant curvature,Tensor(N.S.),2007,68:190-203.
[16]Yoshikawa,R.and Okubo,K.,Constant curvature conditions for Kropina spaces,Balkan J.Geom.Appl.,2012,17(1):115-124.
[17]Yoshikawa,R.and Sabau,S.V.,Kropina metrics and Zermelo navigation on Riemannian manifolds,Geom.Dedicata,2014,171(1):119-148.
[18]Zhang,X.L.and Shen,Y.B.,On Einstein Kropina metrics,Differential Geom.Appl,2013,31:80-92.
[2]Bacso,S.,Cheng,X.Y.and Shen,Z.M.,Curvature properties of(α,β)-metrics,Adv.Stud.Pure Math.,2007,48:73-110.
[3]Chen,G.Z.,Cheng,X.Y.,An important class of conformally flat weak Einstein Finsler metrics,Internat.J.Math.,2013,24(1):Article ID 1350003,15 pages.
[4]Cheng,X.Y.and Shen,Z.M.,Finsler Geometry—An Approach via Randers Spaces,Beijing:Science Press,2012.
[5]Chern,S.S.and Shen,Z.M.,Rieman-Finsler Geometry,Nankai Tracts Math.,Vol.6,Singapore:World Scientific,2005.
[6]Ingarden,R.S.,Geometry of thermodynamics,Diff.Geom.Methods in Theor.Phys.(Doebner,H.D.et al.eds.),XV Intern.Conf.Clausthal,1986,Singapore:World Scientific,1987.
[7]Hojo,S.,Matsumoto,M.and Okubo,K.,Theory of conformally Berwald Finsler spaces and its applications to(α,β)-metrics,Balkan J.Geom.Appl,2000,5(1):107-118.
[8]Kropina,V.K.,On projective Finsler spaces with a certain special form,Naucn.Doklady Vyss.Skoly,Fiz.-Mat.Nauki,1959,2:38-42(in Russian).
[9]Kropina,V.K.,On projective two-dimensional Finsler spaces with a special metric,Trudy Sem.Vektor.Tenzor.Anal.,1961,11:277-292.
[10]Matsumoto,M.and Hojo,S.,A conclusive theorem on C-reducible Finsler spaces,Tensor(N.S.),1978,32:225-230.
[11]Matsumoto,M.,Finsler spaces of constant curvature with Kropina metric,Tensor(N.S.),1991,50:194-201.
[12]Matsumoto,M.,The Berwald connections of a Finsler spaces with(α,β)-metric,Tensor(N.S.),1991,50:18-21.
[13]Shibata,C,On Finsler spaces with Kropina metric,Rep.Math.Phys.,1978,13:117-128.
[14]Xia,Q.L.,On Kropina metrics of scalar flag curvature,Differential Geom.Appl,2013,31:393-404.
[15]Yoshikawa,R.and Okubo,K.,Kropina spaces of constant curvature,Tensor(N.S.),2007,68:190-203.
[16]Yoshikawa,R.and Okubo,K.,Constant curvature conditions for Kropina spaces,Balkan J.Geom.Appl.,2012,17(1):115-124.
[17]Yoshikawa,R.and Sabau,S.V.,Kropina metrics and Zermelo navigation on Riemannian manifolds,Geom.Dedicata,2014,171(1):119-148.
[18]Zhang,X.L.and Shen,Y.B.,On Einstein Kropina metrics,Differential Geom.Appl,2013,31:80-92.