Author(s):  A.V. Bukusheva, candidate of Sciences, associate Professor, National Research Saratov State University named after G.N. Chernyshevsky, Saratov, Russia,

Issue:  Volume 51, № 1

Rubric:  Mathematics

Annotation:  The article is devoted to the study of geometric structures that occur in the distribution of contact manifold. In the previous author`s research almost contact metric structures have been studied. These almost contact metric structures are called extended structures, and are naturally defined on distributions of almost contact and paracontact metric manifolds, bi-metric manifolds, sub-Finsler and sub-Riemannian manifolds. The contact manifold does not have Riemannian metric in contrast to the manifolds listed above. Consequently, the metric tensor of the extended structure is determined due to the symplectic form that fits up the contact structure. The extended almost contact metric structure is defined on the distribution of the contact structure with a fixed internal symplectic connection. The interior invariants of a contact structure with a given interior symplectic connection are distinguished in the article. The following interior invariants are examined: Schouten curvature tensor, the admissible symplectic structure and Wagner-Schouten tensor. The classification of extended structures is carried out in terms of internal invariants. In particular, it is proved that the set of extensions of almost contact metric structures does not contain any cosymplectic and Kenmotsu structures. Besides, the article focuses on the conditions for referring the extended almost contact metric structure to the class C11.

Keywords:  contact structure, almost contact metric structure, interior symplectic connection, skew-symmetric structure, Kenmotsu structure

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