In this paper the author considers a Lorentzian manifold
carrying a time-like concircular unit vector field
, 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
-parallel Ricci tensor or to be
-Einstein manifold and to admit constant scalar curvature. Additionally, some infinitesimal transformations on
are studied and the sectional curvature is obtained.