Almost contact metric structures induced by $G_2$ structures

Abstract

We study almost contact metric structures induced by 2-fold vector cross products on manifolds with G2 structures. We get some results on possible classes of almost contact metric structures. Finally, we give examples.

On symplectic 8-manifolds admitting Spin(7)-structure

“…Using the associative calibration they find a contact 1-form on a 7-manifold with G 2 -structure which satisfies certain compatibility conditions. They also construct explicit almost contact metric structures on manifolds with G 2 -structures which are also studied by Özdemir, Solgun and Aktay in [12].…”

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.…”

Almost paracontact structures obtained fromG2(2)structures

“…Almost contact metric structures induced by G 2 structures were constructed by Matzeu and Munteanu in [7]; see also [1]; and the possible classes that these structures may belong to were considered in [8].…”