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

Citations:

Zbl 0675.53035
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