Slant Submanifolds of a Lorentz Kenmotsu Manifold

Abstract

In this paper, we study slant submanifolds of a Lorentz Kenmotsu manifold. Necessary and sufficient conditions are given on a submanifold of a Lorentz Kenmotsu manifold to be a slant submanifold. We also study slant submanifolds of locally warped product Lorentz Kenmotsu manifold. We give examples of slant submanifold warped product a Lorentz Kenmotsu manifold. In addition, we investigate semi-slant submanifolds of a Lorentz Kenmotsu manifold. Moreover, we show that a semi-slant submanifold of locally warped product Lorentz Kenmotsu manifold is a warped product. Furthermore, we obtain some curvature properties for semi-slant submanifold of a Lorentz Kenmotsu space form. Finally, we show that if a semi-slant submanifold of a Lorentz Kenmotsu space form M is totally geodesic, then M is an $$\eta $$ -Einstein manifold.