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Zbl 0679.53034
Matsumoto, Koji; Mihai, Ion
On a certain transformation in a Lorentzian para-Sasakian manifold.
(English)
[J] Tensor, New Ser. 47, No.2, 189-197 (1988). ISSN 0040-3504

A Lorentzian para-Sasakian (LP-Sasakian) structure is a particular case of a Lorentzian paracontact structure, introduced by the first author in [Bull. Yamagata Univ., Nat. Sci. 12, No.2, 151-156 (1989)]. By analogy with the Sasakian case studied by {\it S. Kato} and {\it M. Nagao} [Kodai Math. J. 18, 87-95 (1966)], in the present paper, the notion of infinitesimal CL-transformation in an LP-Sasakian manifold is defined and a homothetic conformal Killing vector field is obtained. A CL-relation between a symmetric affine connection and the Lorentzian metric connection is studied and the curvature tensor of the Lorentzian metric of a CL-flat LP-Sasakian manifold is obtained.
[C.L.Bejan]
MSC 2000:
*53C15 Geometric structures on manifolds
53B30 Lorentz metrics, indefinite metrics

Keywords: Lorentzian paracontact structure; infinitesimal CL-transformation; Sasakian manifold

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