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.
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Supported by funds of the Universitá del Salento and of the M.I.U.R. (within PRIN 2010–2011).
Dedicated to my grand-daughter Elisa
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Perrone, D. Contact Pseudo-Metric Manifolds of Constant Curvature and CR Geometry. Results. Math. 66, 213–225 (2014). https://doi.org/10.1007/s00025-014-0373-7
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DOI: https://doi.org/10.1007/s00025-014-0373-7