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http://dx.doi.org/10.4134/CKMS.2014.29.2.319

CONFORMALLY RECURRENT SPACE-TIMES ADMITTING A PROPER CONFORMAL VECTOR FIELD  

De, Uday Chand (Department of Pure Mathematics University of Calcutta)
Mantica, Carlo Alberto (Physics Department Universita degli Studi di Milano)
Publication Information
Communications of the Korean Mathematical Society / v.29, no.2, 2014 , pp. 319-329 More about this Journal
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 ${\sigma}$, 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 ${\sigma}_j$ 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 ${\sigma}_j$.
Keywords
conformally recurrent space-times; proper conformal vector fields; pseudo-Riemannian manifolds; Weyl compatible tensors; Petrov types; Lorentzian metrics;
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Times Cited By KSCI : 1  (Citation Analysis)
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