Given the Riemann, or the Weyl, or a generalized curvature tensor K, a symmetric tensor b_ij is called compatible with the curvature tensor if b_im K_jklm + b_jm K_kilm +bkm_K_ijlm = 0. In addition to establishing some known and some new properties of such tensors, we prove that they form a special Jordan algebra, i.e. the symmetrized product of K-compatible tensors is K-compatible.
The Jordan algebras of Riemann, Weyl and curvature compatible tensors / C.A. Mantica, L.G. Molinari. - In: COLLOQUIUM MATHEMATICUM. - ISSN 0010-1354. - 167:1(2022), pp. 63-72. [10.4064/cm8067-10-2020]
The Jordan algebras of Riemann, Weyl and curvature compatible tensors
C.A. ManticaCo-primo
;L.G. Molinari
Co-primo
2022
Abstract
Given the Riemann, or the Weyl, or a generalized curvature tensor K, a symmetric tensor b_ij is called compatible with the curvature tensor if b_im K_jklm + b_jm K_kilm +bkm_K_ijlm = 0. In addition to establishing some known and some new properties of such tensors, 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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