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On Lorentzian almost paracontact manifolds with a structure of the concircular type. (English) Zbl 1054.53056
In this paper the author considers a Lorentzian manifold $M$ carrying a time-like concircular unit vector field $\xi$, that is a Lorentzian almost paracontact manifold with a structure of the concircular type. The notion first introduced by K. Matsumoto [Bull. Yamagata Univ., Nat. Sci. 12, No. 2, 151–156 (1989; Zbl 0675.53035)]. There are given conditions for such a manifold $M$ to have $\eta$-parallel Ricci tensor or to be $\eta$-Einstein manifold and to admit constant scalar curvature. Additionally, some infinitesimal transformations on $M$ are studied and the sectional curvature is obtained.

##### MSC:
 53C15 Differential geometric structures on manifolds 53C40 Global submanifolds (differential geometry)