Abstract:There is one-to-one correspondence between contact semi-Riemannian structures ( η , ξ , φ , g ) and non-degenerate almost CR structures ( H , ϑ , J ) . In general, a non-degenerate almost CR structure is not a CR structure, that is, in general the integrability condition for H 1 , 0 : = X - i J X , X ∈ H is not satisfied. In this paper we give a survey on some known results, with the addition of some new results, on the geometry of contact semi-Riemannian manifolds, also in the con… Show more
We study the geometry of almost contact pseudo-metric manifolds in terms of tensor fields h := 1 2 £ ξ ϕ and ℓ := R(·, ξ)ξ, emphasizing analogies and differences with respect to the contact metric case. Certain identities involving ξ-sectional curvatures are obtained. We establish necessary and sufficient condition for a nondegenerate almost CR structure (H(M ), J, θ) corresponding to almost contact pseudo-metric manifold M to be CR manifold. Finally, we prove that a contact pseudometric manifold (M, ϕ, ξ, η, g) is Sasakian if and only if the corresponding nondegenerate almost CR structure (H(M ), J) is integrable and J is parallel along ξ with respect to the Bott partial connection.Mathematics Subject Classification (2010). 53C15; 53C25; 53D10.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.