In this paper, we study the geometry of a semi-Riemannian manifold M̄ of quasi-constant curvature. The main result is two characterization theorems for M̄ endowed with a statical, screen homothetic or screen totally umbilical half lightlike submanifold M . Mathematics Subject Classification: 53C25, 53C40, 53C50

In this study, we introduce indefinite sasakian statistical manifolds and lightlike hypersurfaces of an manifold. Some relations among induced geometrical objects with respect to dual connections in a hypersurface manifold are obtained. examples related these concepts also presented. Finally, prove that invariant submanifold is

Suppose that (M, G) is a Riemannian manifold and f : M → R is a submersion. Then the complete lift of f, f : TM → R defined by f = ∂f ∂xi y is also a submersion. This interesting case leads us to the investigation of the level hypersurfaces of f as a submanifold of tangent bundle TM . In addition, we prolonge the level hypersurfaces of f to N̄ = (f)(0). Also, under the condition ∇̂f is a constant...