## 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 General geometric structures on manifolds (almost complex, almost product structures, etc.) 53C40 Global submanifolds

Zbl 0675.53035