Geometric Classification of Warped Products Isometrically Immersed into Conformal Sasakian Space Froms

Abstract

Warped products play important roles in differential geometry, general relativity, and symmetry science. In this paper, we study the warped product pointwise semi-slant submanifolds that are isometrically immersed into conformal Sasakian space form. We show that there does not exist any proper warped product pointwise semi-slant submanifolds in conformal Sasakian manifolds. We derived some geometric inequalities for squared norm of second fundamental form from a warped product pointwise semi-slant submanifold into a conformal Sasakian manifolds.

Keywords

• warped product
• pointwise semi-slant submanifolds
• conformal Sasakian space form