Two subclasses of generalized Kenmotsu manifolds

Abstract

The paper studies the geometry of the Riemann curvature tensor of generalized Kenmotsu manifolds. In this paper, several identities satisfied by the curvature tensor of generalized Kenmotsu manifolds are obtained. Two identities are distinguished from the obtained identities, called the first and second additional identities of curvature of the GK-manifold. Based on additional identities, two subclasses of GK-manifolds are distinguished, and a local characterization of the distinguished classes is also obtained. It is proved that the distinguished two subclasses of GK-manifolds coincide and have dimension 5. In addition, it is proved that the class of distinguished manifolds coincides with the class of almost contact metric manifolds obtained from a cosymplectic manifold by a canonical concircular transformation of a cosymplectic structure of dimension 5.

Об Обобщенных Многообразиях Кенмоцу Как Гиперповерхностях Многообразий Вайсмана - Грея

“…Definition 3 [14]. A generalized Kenmotsu manifold (shortly, GK-manifold) is an ACMmanifold (M 2n+1 , Φ, ξ, η, g) which satisfies the following identity:…”

Tensor invariants of generalized Kenmotsu manifolds

“…The following takes place Proposition 1.1 [22]. Structural tensors of the AC-structure have the following properties: [9], [12]). The class of almost contact metric manifolds characterized by the identity…”

“…In the paper [12], identities of curvature of SGK-manifolds of the second type were obtained, and on their basis some subclasses of SGK-manifolds of the second type were distinguished. The form of the tensor of the holomorphic sectional curvature of SGKmanifolds of the second type of class 4 is obtained and it is proved that SGK-manifolds of the second type of class 5 are Kenmotsu manifolds.…”

Curvature Identities for Generalized Kenmotsu Manifolds

“…In [19], we obtained several identities for the Riemannian curvature tensor of generalized Kenmotsu manifolds and separated two subclasses of GK-manifolds. In addition, there were obtained the local structure of separated classes for GK-manifolds.…”

“…In [20], two classes of generalized Kenmotsu manifolds were separated, called the class of f-holomorphic and the class of f-paracontact manifolds; a complete classification of the separated classes was obtained. In this paragraph we will also, as in [19] and [20], consider two classes of generalized Kenmotsu manifolds. Definition 4.1.…”