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Collineations of a symmetric 2-covariant tensor: Ricci collineations. (English) Zbl 1287.83017

Summary: The infinitesimal transformations that leave invariant a two-covariant symmetric tensor are studied. The interest of these symmetry transformations lays in the fact that this class of tensors includes the energy-momentum and Ricci tensors. We find that in most cases the class of infinitesimal generators of these transformations is a finite dimensional Lie algebra, but in some cases exhibiting a higher degree of degeneracy, this class is infinite dimensional and may fail to be a Lie algebra. As an application, we study the Ricci collineations of a type B warped spacetime.{
©2013 American Institute of Physics}

MSC:

83C20 Classes of solutions; algebraically special solutions, metrics with symmetries for problems in general relativity and gravitational theory
53Z05 Applications of differential geometry to physics
83C40 Gravitational energy and conservation laws; groups of motions
17B45 Lie algebras of linear algebraic groups
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