Classification of second order symmetric tensors in five-dimensional Kaluza–Klein-type theories

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  • J. Santos
    Universidade Federal do Rio G. do Norte, Departamento de Física, Caixa Postal 1641, 59072-970 Natal-RN, Brazil
  • M. J. Rebouças
    Centro Brasileiro de Pesquisas Físicas, Departamento de Relatividade e Partículas, Rua Dr Xavier Sigaud, 150, 22290-180 Rio de Janeiro-RJ, Brazil
  • A. F. F. Teixeira
    Centro Brasileiro de Pesquisas Físicas, Departamento de Relatividade e Partículas, Rua Dr Xavier Sigaud, 150, 22290-180 Rio de Janeiro-RJ, Brazil

Abstract

<jats:p>An algebraic classification of second order symmetric tensors in five-dimensional Kaluza–Klein-type Lorentzian spaces is presented by using Jordan matrices. It is shown that the possible Segre types are [1,1111], [2111], [311], [zz̄111], and the degeneracies thereof. A set of canonical forms for each Segre type is found. The possible continuous groups of symmetry for each canonical form are also studied.</jats:p>

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