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# Curvature of $K$-contact Semi-Riemannian Manifolds

Published:2013-07-22
Printed: Jun 2014
• Domenico Perrone,
Universitá del Salento, Dipartimento di Matematica e Fisica ‟E. De Giorgi”, Via Provinciale Lecce-Arnesano, 73100 Lecce, Italy
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## Abstract

In this paper we characterize $K$-contact semi-Riemannian manifolds and Sasakian semi-Riemannian manifolds in terms of curvature. Moreover, we show that any conformally flat $K$-contact semi-Riemannian manifold is Sasakian and of constant sectional curvature $\kappa=\varepsilon$, where $\varepsilon =\pm 1$ denotes the causal character of the Reeb vector field. Finally, we give some results about the curvature of a $K$-contact Lorentzian manifold.
 Keywords: contact semi-Riemannian structures, $K$-contact structures, conformally flat manifolds, Einstein Lorentzian-Sasaki manifolds
 MSC Classifications: 53C50 - Lorentz manifolds, manifolds with indefinite metrics 53C25 - Special Riemannian manifolds (Einstein, Sasakian, etc.) 53B30 - Lorentz metrics, indefinite metrics

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