Farah Hasan Jasim AlHusseini

This study aims to investigate the quasi-conformal curvature tensor of NC10-manifold. The components of this tensor were determined using the adjoined G-structure space. Three quasi-conformal invariants were identified in relation to the vanishing quasi-conformal curvature tensor. Subsequently, three types of NC10-manifold were established. Furthermore, the necessary conditions for these classes to be an η-Einstein manifold were established.

Abstract: The authors classified a locally conformal almost cosympleсtic manifold ( L C A C S -manifold) according to the conharmonic curvature tensor. In particular, they have determined the necessary conditions for a conharmonic curvature tensor on the L C A C S -manifold of classes C T i , i = 1 , 2 , 3 to be Φ -quaisi invariant. Moreover, it has been proved that any L C A C S -manifold of the class C T 1 is conharmoniclly Φ -paracontact.

The main purpose of the present paper is to study the geometric properties of the conharmonic curvature tensor of normal locally conformal almost cosymplectic manifolds (normal LCAC-manifold). In particular, three conhoronic invariants are distinguished with regard to the vanishing conharmonic tensor. Subsequentaly, three classes of normal LCAC-manifolds are established. Moreover, it is proved that the manifolds of these classes are $ \eta $-Einstein manifolds of type $ (\alpha,\beta) $. Furthermore, we have determined $ \alpha $ and $ \beta $ for each class.

This paper aims to study the geometrical properties of the conharmonic curvature tensor of a locally conformal almost cosymplectic manifold. The necessary and sufficient conditions for the conharmonic curvature tensor to be flat, the locally conformal almost cosymplectic manifold to be normal and an η -Einstein manifold were determined.

In this article, we introduced the concept of holomorphic sectional conharmonic tensor of a normal local conformally almost co-symplectic manifold ( -manifold). In particular, we established some of its properties and analytical expressions. Consequently, analytical conditions for the -manifold to be a kind of point wise constancy conharmoniclly holomorphic sectional are obtained.

The purpose of the present paper is to discuss the geometrical properties of a locally conformal almost cosymplectic manifold of constant curvature. In particular, the necessary and sufficient conditions for the aforementioned manifold to be of constant curvature have been determined.

The aim of the present paper is to study the geometry of locally conformal almost cosymplectic manifold of -holomorphic sectional conharmonic curvature tensor. In particular, the necessary and sucient conditions that locally conformal almost cosymplectic manifold is a manifold of point constant -holomorphic sectional conharmonic curvature tensor have been found. The relation between the mentioned manifold and the Einstein manifold is determined.