On the geometry of nearly trans-Sasakian manifolds

Geometry of Harmonic Nearly Trans-Sasakian Manifolds

“…In [5], almost contact metric structures were considered, which are a linear extension of almost Hermitian structures of the class W 1 ⊕ W 4 in Gray-Herwell classification. Such structures are called nearly trans-Sasakian structures.…”

“…Such structures are called nearly trans-Sasakian structures. In addition, in [5], the authors single out a special class of nearly trans-Sasakian manifolds. A nearly trans-Sasakian structure with a closed contact form is called the eigen nearly trans-Sasakian structure.…”

“…A nearly trans-Sasakian structure with a closed contact form is called the eigen nearly trans-Sasakian structure. In [5], a criterion is proved for when an almost contact metric structure is an eigen nearly trans-Sasakian structure. It is proved that the class of nearly trans-Sasakian manifolds with non-closed contact form coincides with the class of almost contact metric manifolds homothetic to Sasaki manifolds.…”

“…The most important examples of such manifolds are Kenmotsu manifolds and special generalized Kenmotsu manifolds of the second kind. Theorem 3.16 from [5] is of interest: The class of nearly trans-Sasakian manifolds with a closed contact form and a closed Lee form coincides with the class of almost contact metric manifolds, with a closed contact form locally conformal to closely cosymplectic manifolds.…”

“…In this article, we are interested in the class of harmonic nearly trans-Sasakian manifolds, i.e., nearly trans-Sasakian manifolds with a harmonic contact form. The concept of harmonic nearly trans-Sasakian manifolds was introduced in [5,13]. The main purpose of this work is to study the local structure of harmonic nearly trans-Sasakian manifolds.…”