| On Torsion—free Connections in Finsler Geometry |
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| 引用本文： | 郭瑞芝.On Torsion—free Connections in Finsler Geometry[J].数学季刊,1997,12(1):98-103. |
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| 作者姓名： | 郭瑞芝 |
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| 作者单位： | Department of Mathematics，Hunan Normal University，Changsha，410081 |
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| 摘 要： | 61.IntroductionI,etMbeasmoothnudimensionalmanifoldandTMdenoteitstangentt,undIe.AFinslerstructureonMisamapF:TM-O, oo)whichhasthefollowingproperties:(a)FissmoothonTM\{o}.(b)F(x,ty)=ItlF(x,y).(jw,y)eTM\{O},tej{.(c)ThenXnmatr1x(ee(2',y))isposlt1vedefiniteforally/O.AFinslermanifoldisamanifoldwithaFinslerstructure.ItisquiteapparentthattheLevl-C1vitaconnectlonplaysanlmportantroleintheRieman-niangeon1etryofmanifolds.Thusnodoubt,itisnaturaltointreduceconnectionsinFinslergeometry.Manyconnec…
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| 关 键 词： | Finsler几何 无挠联络 Finsler流形 |
On Torsion-free Connections in Finsler Geometry |
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| Guo Ruizhi.On Torsion-free Connections in Finsler Geometry[J].Chinese Quarterly Journal of Mathematics,1997,12(1):98-103. |
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| Authors: | Guo Ruizhi |
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| Abstract: | We introduce a fundamental connection in Finsler geometry,which is torsion-free and almost compatible with the induced metric. We give the difference between this connection and other known connections. |
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| Keywords: | Finsler structure Cartan tensor Cartan/ Berwald/ Chern/ Shen connection h-curvature hv-curvature |
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