Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

SIGMA 12 (2016), 063, 12 pages      arXiv:1602.03693      https://doi.org/10.3842/SIGMA.2016.063

Symmetries of Lorentzian Three-Manifolds with Recurrent Curvature

Giovanni Calvaruso a and Amirhesam Zaeim b
a) Dipartimento di Matematica e Fisica ''E. De Giorgi'', Università del Salento, Prov. Lecce-Arnesano, 73100 Lecce, Italy
b) Department of Mathematics, Payame Noor University, P.O. Box 19395-3697, Tehran, Iran

Received February 12, 2016, in final form June 17, 2016; Published online June 26, 2016

Abstract
Locally homogeneous Lorentzian three-manifolds with recurrect curvature are special examples of Walker manifolds, that is, they admit a parallel null vector field. We obtain a full classification of the symmetries of these spaces, with particular regard to symmetries related to their curvature: Ricci and matter collineations, curvature and Weyl collineations. Several results are given for the broader class of three-dimensional Walker manifolds.

Key words: Walker manifolds; Killing vector fields; affine vector fields; Ricci collineations; curvature and Weyl collineations; matter collineations.

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