Pointwise slant and pointwise semi-slant submanifolds in almost contact metric manifolds

Abstract: As a generalization of slant submanifolds and semi-slant submanifolds, we introduce the notions of pointwise slant submanifolds and pointwise semi-slant sunmanifolds of an almost contact metric manifold. We obtain a characterization at each notion, investigate the topological properties of pointwise slant submanifolds, and give some examples of them. We also consider some distributions on cosymplectic, Sasakian, Kenmotsu manifolds and deal with some properties of warped product pointwise semi-slant submanifolds. Finally, we give some inequalities for the squared norm of the second fundamental form in terms of a warping function and a semi-slant function for warped product submanifolds of cosymplectic, Sasakian, Kenmotsu manifolds.