  Recently, B.-Y. Chen and O. J. Garay studied pointwise slant submanifolds of
almost Hermitian manifolds. By using the notion of pointwise slant
submanifolds, we investigate the geometry of pointwise semi-slant submanifolds
and their warped products in Sasakian and cosymplectic manifolds. We prove that
there exist no proper pointwise semi-slant warped product submanifold other
than contact CR-warped products in Sasakian manifolds. We give non-trivial
examples of such submanifolds in cosypmlectic manifolds and obtain several
fundamental results, including a characterization for warped product pointwise
semi-slant submanifolds.
