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As a generalization of slant submanifolds and semi-slant submanifolds, weintroduce the notions of pointwise slant submanifolds and pointwise semi-slantsunmanifolds of an almost contact metric manifold. We obtain a characterizationat each notion, investigate the topological properties of pointwise slantsubmanifolds, and give some examples of them. We also consider somedistributions on cosymplectic, Sasakian, Kenmotsu manifolds and deal with someproperties of warped product pointwise semi-slant submanifolds. Finally, wegive some inequalities for the squared norm of the second fundamental form interms of a warping function and a semi-slant function for warped productsubmanifolds of cosymplectic, Sasakian, Kenmotsu manifolds.

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