| 曲率与挠率张量的特殊关系 |
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| 引用本文： | 卢卫君,方丽菁,付海平. 曲率与挠率张量的特殊关系[J]. 广西大学学报(自然科学版), 2009, 34(4) |
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| 作者姓名： | 卢卫君 方丽菁 付海平 |
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| 作者单位： | 广西民族大学数学与计算机科学学院,广西,南宁,530006;南昌大学数学系,江西,南昌,330047 |
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| 基金项目： | 国家自然科学资金资助项目,广西科学资金资助项目 |
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| 摘 要： | 研究挠率和曲率张量在Bianchi恒等式中的相依关系,从Cartan结构方程出发,得到了Bianchi恒等式的三种等价表达形式,局部上和整体上证明了曲率、挠率分量满足的关系式,还揭示了第二Bianchi恒等式的降阶表达形式蕴含的物理意义.
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| 关 键 词： | 曲率张量 挠率张量 Bianchi恒等式 张量场的散度 |
Particular relationship between curvature and torsion tensor |
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| LU Wei-jun,FANG Li-jing,FU Hai-ping. Particular relationship between curvature and torsion tensor[J]. Journal of Guangxi University(Natural Science Edition), 2009, 34(4) |
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| Authors: | LU Wei-jun FANG Li-jing FU Hai-ping |
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| Affiliation: | 1.College of Mathematics and Computer Science;Guangxi University for Nationalities;Nanning 530006;China;2.Department of Mathematics;Nanchang University;Nanchang 330031;China |
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| Abstract: | The mutually dependent relations between torsion and curvature tensor in Bianchi identity are studied.From Cantan's structure equations,three equivalent expressions of Bianchi identity are obtained.The behavior of components of torsion and curvature in Bianchi identity is locally revealed.Furthermore,the phisical essence with respect to lower degree expression of the second Bianchi identity is pointed out. |
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| Keywords: | curvature tensor torsion tensor expressions of Bianchi identity divergence of tensor field |
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