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Abstract: A definition is suggested for affine symmetry tensors, which generalize thenotion of affine vectors in the same way that conformal Killing tensorsgeneralize conformal Killing vectors. An identity for these tensors isproved, which gives the second derivative of the tensor in terms of thecurvature tensor, generalizing a well-known identity for affine vectors.Additionally, the definition leads to a good definition of homothetic tensors.The inclusion relations between these types of tensors are exhibited. Therelationship between affine symmetry tensors and solutions to the equation ofgeodesic deviation is clarified, again extending known results about Killingtensors.



Author: Samuel A. Cook, Tevian Dray

Source: https://arxiv.org/







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