On conformally flat LP-Sasakian manifolds with a coefficient \(\alpha\)
The notion of a Lorentzian almost paracontact manifold with a coefficient \(\alpha\) was introduced by \textit{U. C. De}, \textit{A. A. Shaikh} and \textit{A. Sengupta} [Kyungpook Math. J. 42, 177--186 (2002; Zbl 1022.53040)], a generalization of the Lorentzian almost paracontact manifold first introduced in 1989 by \textit{K. Matsumoto} [Bull. Yamagata Univ. Nat. Sci. 12, 151--156 (1989; Zbl 0675.53035)]. In the present paper the authors study a conformally flat LP-Sasakian manifold \(M_n\) with a coefficient \(\alpha\). It is shown that the characteristic vector field \(\xi\) is a concircular vector field if and only if \(M_n\) \((n> 3)\) is \(\eta\)-Einstein. Particularly, \(M_3\) is always an \(\eta\) Einstein manifold, if \(\alpha\) is constant. Moreover, \(M_n\) is of constant sectional curvature, if the scalar curvature is constant.
scientific article; zbMATH DE number 1932198