Almost paracontact structures obtained fromG2(2)structures

Abstract

In this paper, we construct almost paracontact metric structures by using the fundamental 3-forms of manifolds with G * 2(2) structures. The existence of certain almost paracontact metric structures is investigated due to the properties of the 2-fold vector cross-product. Furthermore, we give some relations between the classes of G * 2(2) structures and almost paracontact metric structures.

Some results on pseudosymmetric normal paracontact metric manifolds

“…For the sake of brevity, a normal paracontact metric manifold is said to be paracontact metric manifold [8].…”

“…In [6], S. Zamkovoy and G. Nakova reviewed the decomposition of almost contact metric manifolds in eleven classes. In addition to almost paracontact metric manifolds, K. Mandal and U.C De in [7], N. Özdemir, S. Aktay and M.solgun in [8] examined paracontact metric manifolds and obtained their various geometric properties. Also, in [9], H. Pandey and A. Kumar examined the anti-invariant submanifolds of almost paracontact manifolds.…”

D-Homothetic Deformations and Almost Paracontact Metric Manifolds

“…Differentiable manifolds having almost paracontact structures were introduced by [5] and after [11] many authors have made contribution, see [7,9,[11][12][13] and references therein. Manifolds with almost paracontact metric structure were classified according to the Levi-Civita covariant derivative of the fundamental tensor.…”

A natural way to construct an almost complex B‐metric structure

“…Also, many authors studied these classes and the relations with other structures. The existence of almost contact metric structures of certain classes that were obtained from G 2 -structures are investigated in Özdemir et al 5 Almost contact metric structures on nilpotent Lie groups of dimension five and the relations between the classification of these structures are studied in Özdemir et al 6 Almost hermitian structures were classified in Gray and Hervella 7 ; almost contact structures with B-metric are classified in Ganchev et al, 8 and in a similar vein, almost complex B-metric structures are classified in Ganchev and Borisov. 9 In this work, we will construct an almost complex B-metric structure from a given almost contact B-metric structure and evaluate some relations between the classes of these structure.…”