Tensor invariants of generalized Kenmotsu manifolds

Abstract

In this paper, we study the properties of generalized Kenmotsu manifolds, consider the second-order differential geometric invariants of the Riemannian curvature tensor of generalized Kenmotsu manifolds (by the symmetry properties of the Riemannian geometry tensor). The concept of a tensor spectrum is introduced. Nine invariants are singled out and the geometric meaning of these invariants turning to zero are investigated. The identities characterizing the selected classes are singled out. Also, 9 classes of generalized Kenmotsu manifolds are distinguished, the local structure of 8 classes from the selected ones is obtained.