Contact Pseudo-Metric Manifolds of Constant Curvature and CR Geometry

Abstract

In this paper, we show that if an integrable contact pseudo-metric manifold of dimension 2n + 1, n ≥ 2, has constant sectional curvature \({\kappa}\), then the structure is Sasakian and \({\kappa=\varepsilon=g(\xi,\xi)}\), where \({\xi}\) is the Reeb vector field. We note that the notion of contact pseudo-metric structure is equivalent to the notion of non-degenerate almost CR manifold, then an equivalent statement of this result holds in terms of CR geometry. Moreover, we study the pseudohermitian torsion \({\tau}\) of a non-degenerate almost CR manifold.