On C5 ⊕ C12 –Manifolds
almost contact metric manifold
Kenmotsu manifolds
Einstein manifold
Cartan’s Structure Equations
Riemannian Curvature tensor
In this paper, we explore the geometric properties and tensor components of C5 ⊕ C12 -manifolds. Firstly, we established the characteristics identity of this class on G-structure adjoined space and found the equivalent conditions for the defining condition of the class in terms of Kirichenko’s tensors. Furthermore, the Cartan structure equations, components of the Riemannian curvature tensor, and the Ricci tensor are derived of this class. Finally, we introduced the appropriate conditions for these manifolds to be Einstein manifolds.