Gerasimenko S.A., Rustanov A.R., Shchipkova N.N.
ANALOGS IDENTITIES GRAY FOR TENSOR CONHARMONIC CURVATURE AC-MANIFOLDS OF CLASS C₁₁ ^{[№ 9 ' 2015]}
The main objective is to study the geometry of the curvature tensor conharmonic AC-class varieties C₁₁. For this purpose, the following two problems are solved: 1) get contact analogues identities Gray conharmonic curvature tensor introduced in consideration of Ishi; 2) on the basis of these identities to isolate and study the subclasses of AC-class varieties C₁₁. The paper identified three classes of almost contact metric manifolds class C₁₁, named as GK₁-, GK₂- and GK₃-manifolds. In Theorem 1 we obtain conditions on the curvature tensor components conharmonic on the space of the associated G-structure in which almost contact metric structure belongs to a class C₁₁ selected classes. Theorem 2 is proved that the variety of AC-class C₁₁ is GK₃-manifold and the GK₂-manifold. In Theorem 3 proved that AC-manifold of class C₁₁, which is GK₁-manifold is a manifold with Einstein's cosmological constant. In particular, in the case of completeness and continuity is compact and has a finite fundamental group. Finally, in Theorem 4 is proved that the variety of AC-class C₁₁ dimension greater than 5 is GK₁-manifold if and only if it is Ricci flat manifold.

Rustanov A.R., Gerasimenko S.A., Shchipkova N.N.
THE GEOMETRY OF TENSOR CONHARMONIC CURVATURE AC-MANIFOLDS OF CLASS C₁₁ ^{[№ 9 ' 2015]}
The main objective is to study the geometry of the curvature tensor conharmonic almost contact metric manifolds class C₁₁. To this end, following tasks: 1) calculate the basic essential components of curvature tensor conharmonic space of the associated G-structure; 2) explore conharmonic flat manifolds of class C₁₁; 3) get the identities satisfied by the curvature tensor conharmonic AC-class varieties C₁₁; 4) select and explore some subclasses of AC-class varieties C₁₁ of differential-geometric invariants of the second order. The paper addressed these problems. We prove the following theorem. Theorem 1: conharmonic flat AC-manifold of class C₁₁ is Ricci-flat manifold. Theorem 2: conharmonic flat AC-manifold of class C₁₁ is a manifold of Einstein. Theorem 3: conharmonic flat AC-manifold of class C₁₁ is a flat manifold. Theorem 4: AC-manifold of class C₁₁ is a manifold of class K₁ if and only if the AC-manifold of class C₁₁ is Ricci-flat manifold. Theorem 5: AC-manifold of class C₁₁ is a manifold of class K₂ if and only if the AC-manifold of class C₁₁ is Ricci-flat manifold. Theorem 6: AC-manifold of class C₁₁ is a manifold of class K₃ if and only if the AC-manifold of class C₁₁ is a flat manifold. Theorem 7: AC-manifold of class C₁₁, a manifold of class K₄ is a manifold of class Einstein's cosmological constant. In particular, in the case of completeness and continuity is compact and has a finite fundamental group. Theorem 8. AC-manifold of class C₁₁ dimension greater than 5 is K₄-manifold if and only if it is Ricci flat manifold.

Rustanov A.R., Shchipkova N.N.
GEOMETRY OF CLASS C11AC-MANIFOLDS CONCIRCULAR CURVATURE TENSOR ^{[№ 9 ' 2014]}
This paper describes the geometry of concircular curvature tensor in AC-manifolds of class C₁₁. We have calculated its components for the space of the associated G-structure, derivated identities satisfied by the concircular curvature tensor. On the basis of these identities allocated some subclasses of AC-manifolds of class C₁₁ and derivated local characterization of selected classes.

Rustanov A.R., Shchipkova N.N.
DIFFERENTIAL GEOMETRY OF CONTACT METRIC MANIFOLDS OF NС₁₁ CLASS ^{[№ 1 ' 2013]}
This paper considers a new class of contact metric manifolds, which generalizes the class of АС-manifolds of the С₁₁ class by the classification of Chinya and Gonzalez. The complete group of structural equations for NC₁₁-manifolds derived, and components of Riemann-Christoffel tensor, Ricci tensor and the scalar curvature are computed basing on these equations. Properties of NC₁₁-manifolds are derived. Some identities of the Riemann curvature tensor are derived, too.

Rustanov A.R., Shchipkova N.N.
CURVATURE IDENTITIES OF CLASS C₁₁ MANIFOLD ^{[№ 6 ' 2011]}
The article deals with the AU-manifold of class C₁₁, which generalize the class of skew-symplectic manifolds. The identities of the curvature of this class manifold are obtained. As a consequence, the expression of the tensor F-sectional curvature tensor by the Riemann — Christoffel tensor was got.

Rustanov A.R., Shchipkova N.N.
THE DIFFERENTIAL GEOMETRY OF THE ALMOST CONTACT METRIC VARIETIES OF THE CLASS S₁₁. ^{[№ 9 ' 2010]}
The work examined the new class of almost contact metric varieties, the generalizing class of cosimplect varieties. The authors got the complete classification of the AS-varieties of the class S₁₁ of a constant F-holomorphic sectional curvature.