| Abstract [eng] |
An almost contact metric structure (φ, ξ, η, g) of the elliptic type and of the second kind is defined in (2n-1)-dimensional manifold M2n-1 by affinor j ϕi , vector ξ i , covector j η and metric gij satisfying the conditions: [...] 1. Such a structure is induced in normalized hypersurfaces M2n-1 of manifolds M2n equipped with almost complex structure F and B-metric G. If Riemannian connection is F-connection, manifold M2n is called the B-space of elliptic type. In the article, 2-parametric set aG+bF, a, b=const, of metrics in M2n is reviewed. The set is defined in the hypersurface M2n-1: a set of almost contact metric structures (φ′, ξ′, η′, g′) of elliptic type of the second kind. The main result of the article is demonstration of the theorem. If M2n is B-space of elliptic type, then normality, integrability, contactness of one structure in the set of almost contact metric structures is equivalent to normality, integrability, contactness, of all structures respectively. |
