The Jordan algebras of Riemann, Weyl and curvature compatible tensors

Carlo Alberto Mantica, Luca Guido Molinari Colloquium Mathematicum MSC: Primary 53B20; Secondary 17C90. DOI: 10.4064/cm8067-10-2020 Published online: 12 April 2021

Abstract

Given the Riemann, or the Weyl, or a generalized curvature tensor $K$, a symmetric tensor $b_{ij}$ is called \emph {compatible} with the curvature tensor if $b_i{}^m K_{jklm} + b_j{}^m K_{kilm} + b_k{}^m K_{ijlm}=0$. 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.

Authors

  • Carlo Alberto ManticaI.I.S. Lagrange
    Via L. Modignani 65
    20161 Milano, Italy
    and
    I.N.F.N. sezione di Milano
    Via Celoria 16
    20133 Milano, Italy
    e-mail
  • Luca Guido MolinariPhysics Department Aldo Pontremoli
    Università degli Studi di Milano
    Via Festa del Perdono 7
    20122 Milano, Italy
    and
    I.N.F.N. sezione di Milano
    Via Celoria 16
    20133 Milano, Italy
    e-mail

Search for IMPAN publications

Query phrase too short. Type at least 4 characters.

Rewrite code from the image

Reload image

Reload image