Quadratic Lagrangians and Palatini's device
Quadratic Lagrangians and Palatini's device
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二次拉格朗日和帕拉蒂尼装置
DOI：
10.1088/0305-4470/12/8/017
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发表时间：
1979
期刊：
影响因子：
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通讯作者：
H. Buchdahl
中科院分区：
文献类型：
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作者：
H. Buchdahl
本文讨论了作用量S的g-变差与P-变差的相互不等价性，并要求线性联络Gamma mkl的分量是对称的。在g变分下，S需要相对于度量张量gij的变化是平稳的，Gamma mkl从一开始就被认为是Christoffel符号，而在P变分下，gij和Gamma mkl最初被认为是相互独立的，S需要相对于这些量的独立变化是平稳的。讨论说明长度的例子中，S的拉格朗日是一个或另一个一组齐次或非齐次二次不变量的黎曼张量。
The author deals with the mutual inequivalence of g-variation and P-variation of a given action S, the components of linear connection Gamma mkl being required to be symmetric. Under g-variation S is required to be stationary with respect to variations of the metric tensor gij, the Gamma mkl being taken to be Christoffel symbols from the outset, whereas under P-variations the gij and Gamma mkl are initially regarded as mutually independent of S is required to be stationary with respect to independent variations of these quantities. The discussion is illustrated at length by examples in which the Lagrangian of S is one or another of a set of homogeneous or inhomogeneous quadratic invariants of the Riemann tensor.