CONFORMALLY RECURRENT SPACE-TIMES ADMITTING A PROPER CONFORMAL VECTOR FIELD

Title & Authors
CONFORMALLY RECURRENT SPACE-TIMES ADMITTING A PROPER CONFORMAL VECTOR FIELD
De, Uday Chand; Mantica, Carlo Alberto;

Abstract
In this paper we study the properties of conformally recurrent pseudo Riemannian manifolds admitting a proper conformal vector field with respect to the scalar field $\small{{\sigma}}$, focusing particularly on the 4-dimensional Lorentzian case. Some general properties already proven by one of the present authors for pseudo conformally symmetric manifolds endowed with a conformal vector field are proven also in the case, and some new others are stated. Moreover interesting results are pointed out; for example, it is proven that the Ricci tensor under certain conditions is Weyl compatible: this notion was recently introduced and investigated by one of the present authors. Further we study conformally recurrent 4-dimensional Lorentzian manifolds (space-times) admitting a conformal vector field: it is proven that the covector $\small{{\sigma}_j}$ is null and unique up to scaling; moreover it is shown that the same vector is an eigenvector of the Ricci tensor. Finally, it is stated that such space-time is of Petrov type N with respect to $\small{{\sigma}_j}$.
Keywords
conformally recurrent space-times;proper conformal vector fields;pseudo-Riemannian manifolds;Weyl compatible tensors;Petrov types;Lorentzian metrics;
Language
English
Cited by
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