A classification of almost contact metric manifolds

Abstract

It is obtained a complete classi/ication /or almost contaet metric mani/olds through the study o/ the cavariant derivative o] the ]undamental 2-]orm on those mani/otds. O. -Introduction.

Almost contact metric structures induced by $G_2$ structures

“…In [7], a classification of almost contact metric manifolds was obtained via the study of the covariant derivative of the fundamental 2-form. Let (ξ, η, g) be an almost contact metric structure on R 2n+1 .…”

Almost Contact Metric Structures on 5-Dimensional Nilpotent Lie Algebras

“…In [7], a classification of almost contact metric manifolds was obtained via the study of the covariant derivative of the fundamental two-form. A space having the same symmetries as the covariant derivative of the fundamental two-form was written, and, then, this space was decomposed into twelve U(n) × 1 irreducible components C 1 , .…”

“…For example, the trivial class for which ∇Φ = 0 [8], corresponds to the class of cosymplectic (called co-Kähler by some authors) manifolds, C 1 is the class of nearly-K-cosymplectic manifolds, etc. [7]. For classification of almost contact metric structures (see also [9]).…”

“…"Almost cosymplectic", "cosymlectic" and "α-Kenmotsu" structures in our paper correspond to "almost co-Kähler", "co-Kähler" and "α co-Kähler" in [5], respectively. Throughout the paper, the definitions in and [7,8] will be followed.…”

A Family of Characteristic Connections

“…The non-integrable geometries are studied by many mathematicians ( [5], [6], [9]) and a very important tool in studying non-integrable geometries is the characteristic connection ( [7]). The characteristic connection is a metric connection with a skew symmetric torsion which preserves a given G-structure.…”