Structures on the Product of Two Almost Hermitian Almost Contact Manifolds (original) (raw)

Almost Hermitian structures on the products of two almost contact metric manifolds

In this paper, we study the almost Hermitian structure on the product of two almost contact metric manifolds. We give some properties that each factor should satisfy to make the almost Hermitian structure on the product manifold in a certain class of almost Hermitian manifolds. In addition, opposite to Chinea-Gonzales, we show that semi-cosymplectic manifolds do not contain the class C 12. M.S.C. 2010: 53D10, 57R15.

Manifolds with almost contact 3-structure and metrics of Hermitian-Norden type

It is introduced a differentiable manifold with almost contact 3-structure which consists of an almost contact metric structure and two almost contact B-metric structures. The corresponding classifications are discussed. The product of this manifold and a real line is an almost hypercomplex manifold with Hermitian-Norden metrics. The vanishing of the Nijenhuis tensors and their associated tensors is considered. It is proven that the introduced manifold of cosymplectic type is flat. Some examples of the studied manifolds are given.

Almost contact metric manifolds with certain condition

The object of this article is to study a new class of almost contact metric structures which are integrable but non normal. Illustrativeexamples are given. Mathematics Subject Classification (2010). Primary 53C15; Secondary 53C55.

Almost contact metric structures induced by G_2G_2G_2 structures

TURKISH JOURNAL OF MATHEMATICS, 2017

We study almost contact metric structures induced by 2-fold vector cross products on manifolds with G 2 structures. We get some results on possible classes of almost contact metric structures. Finally we give examples.

Classification of Almost Contact Metric Structures on 3D Lie Groups

Journal of Mathematical Sciences, 2023

We study almost contact metric structures on 3-dimensional Lie algebras and investigate the class of left invariant almost contact metric structures on the corresponding Lie groups. We introduce a general approach and we obtain a full classification in dimension three.

Almost contact structures and curvature tensors

Kodai Mathematical Journal, 1981

We determine an orthogonal decomposition of the vector space of some curvature tensors on a co-Hermitian real vector space, in irreducible components with respect to the natural induced representation of c U(n)xl.

Almost Hermitian structures and quaternionic geometries

Differential Geometry and its Applications, 2004

Gray & Hervella gave a classification of almost Hermitian structures (g, I) into 16 classes. We systematically study the interaction between these classes when one has an almost hyper-Hermitian structure (g, I, J, K). In general dimension we find at most 167 different almost hyper-Hermitian structures. In particular, we obtain a number of relations that give hyperKäher or locally conformal hyperKähler structures, thus generalising a result of Hitchin. We also study the types of almost quaternion-Hermitian geometries that arise and tabulate the results.

On 3-DIMENSIONAL Normal Almost Contact Metric Manifolds Satisfying Certain Curvature Conditions

Communications of the Korean Mathematical Society, 2009

The object of the present paper is to study 3-dimensional normal almost contact metric manifolds satisfying certain curvature conditions. Among others it is proved that a parallel symmetric (0, 2) tensor field in a 3-dimensional non-cosympletic normal almost contact metric manifold is a constant multiple of the associated metric tensor and there does not exist a non-zero parallel 2-form. Also we obtain some equivalent conditions on a 3-dimensional normal almost contact metric manifold and we prove that if a 3-dimensional normal almost contact metric manifold which is not a β-Sasakian manifold satisfies cyclic parallel Ricci tensor, then the manifold is a manifold of constant curvature. Finally we prove the existence of such a manifold by a concrete example.

A Study of New Class of Almost Contact Metric Manifolds of Kenmotsu Type

Tamkang Journal of Mathematics, 2021

In this paper, we characterized a new class of almost contact metric manifolds and established the equivalent conditions of the characterization identity in term of Kirichenko’s tensors. We demonstrated that the Kenmotsu manifold provides the mentioned class; i.e., the new class can be decomposed into a direct sum of the Kenmotsu and other classes. We proved that the manifold of dimension 3 coincided with the Kenmotsu manifold and provided an example of the new manifold of dimension 5, which is not the Kenmotsu manifold. Moreover, we established the Cartan’s structure equations, the components of Riemannian curvature tensor and the Ricci tensor of the class under consideration. Further, the conditions required for this to be an Einstein manifold have been determined.