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arXiv · 1910.03929

The Jordan algebras of Riemann, Weyl and curvature compatible tensors

Carlo Alberto Mantica·Luca Guido Molinari
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Abstract

Given the Riemann, or the Weyl, or a generalized curvature tensor K, a symmetric tensor $b_{ij}$ is named `compatible' with the curvature tensor if $b_i{}^m K_{jklm} + b_j{}^m K_{kilm} + b_k{}^m K_{ijlm} = 0$. Amongst showing known and new properties, we prove that they form a special Jordan algebra, i.e. the symmetrized product of K-compatible tensors is K-compatible.

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Carlo Alberto Mantica, Luca Guido Molinari. 2019-10-08. The Jordan algebras of Riemann, Weyl and curvature compatible tensors. https://doi.org/10.4064/cm8067-10-2020

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