Four-dimensional Tensor Identities of Low Order for the Weyl and Ricci Tensors

S. Brian Edgar

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Four-dimensional Tensor Identities of Low Order for the Weyl and Ricci Tensors

机译：Weyl和Ricci张量的低阶四维张量恒等式

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It is shown that the new tensor identity recently discovered by Bonanos, and some other tensor identities recently investigated, are consequences of a very simple and mathematically trivial (but subtle) identity high-lighted some years ago by Lovelock, Lovelock's identity gives a tensor identity of first order in Weyl-like tensors, and a tensor identity of second order in Ricci-like tensors, from which higher order identities, such as those recently studies, can easily be constructed.

机译：结果表明，Bonanos最近发现的新张量身份以及最近研究的其他一些张量身份，是洛夫洛克几年前强调的非常简单且数学上微不足道（但微妙）的身份的结果，洛夫洛克的身份给出了张量身份Weyl型张量中的一阶张量恒等式和Ricci类张量中的二阶张量恒等式，从中可以轻松地构造更高阶的恒等，例如最近研究的恒等式。

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《General Relativity and Gravitation: GRG Journal》 |1999年第3期|共7页
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S. Brian Edgar;
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1. ON SHRINKING GRADIENT RICCI SOLITONS WITH POSITIVE RICCI CURVATURE AND SMALL WEYL TENSOR [J] . Zhuhong ZHANG, Chih-Wei CHEN 数学物理学报（英文版） . 2019,第005期
2. Four-dimensional Tensor Identities of Low Order for the Weyl and Ricci Tensors [J] . S. Brian Edgar General Relativity and Gravitation: GRG Journal . 1999,第3期

机译：Weyl和Ricci张量的低阶四维张量恒等式
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Four-dimensional Tensor Identities of Low Order for the Weyl and Ricci Tensors

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