Some properties of Riemannian spaces of quasi-constant curvature (Q2771169)

The spaces of quasi-constant curvature have been introduced by \textit{V. Boju} and \textit{M. Popescu} [J. Differ. Geom. 13, 373-383 (1978; Zbl 0421.53033)] as a special case of Chern-Vranceanu spaces [\textit{V. Boju, M. Popescu} and \textit{I. Virlan}, An. Univ. Craiova, Ser. Mat. Fiz.-Chim. 6, 89-96 (1978; Zbl 0454.53017)]. In the present paper, the authors study the \(n\)-dimensional Riemannian spaces considered by \textit{B.-Y. Chen} and \textit{K. Yano} [Tensor, New Ser. 26, 318-322 (1972; Zbl 0257.53027)], defined as follows: a conformally flat space \(M\) whose curvature tensor verifies an equation depending of two differentiable functions \(a\), \(b\) and of some unit vector field \(v\), called the generator of the space. Finally is proved that every simply connected space of this type, such that \(a\) is not constant, is the warped product of an open interval and a space of constant curvature.