Certain results on almost contact pseudo-metric manifolds

Abstract

We study the geometry of almost contact pseudo-metric manifolds in terms of tensor fields $$h:=\frac{1}{2}\pounds _\xi \varphi $$ and $$\ell := R(\cdot ,\xi )\xi $$ , emphasizing analogies and differences with respect to the contact metric case. Certain identities involving $$\xi $$ -sectional curvatures are obtained. We establish necessary and sufficient condition for a nondegenerate almost CR structure $$(\mathcal {H}(M), J, \theta )$$ corresponding to almost contact pseudo-metric manifold M to be CR manifold. Finally, we prove that a contact pseudo-metric manifold $$(M, \varphi ,\xi ,\eta ,g)$$ is Sasakian pseudo-metric if and only if the corresponding nondegenerate almost CR structure $$(\mathcal {H}(M), J)$$ is integrable and J is parallel along $$\xi $$ with respect to the Bott partial connection.