  The aim of the present paper to define and study semi-slant
$\xi^\perp-$Riemannian submersions from Sasakian manifolds onto Riemannian
manifolds as a generalization of anti-invariant $\xi^\perp-$Riemannian
submersions, semi-invariant $\xi^\perp-$Riemannian submersions and slant
Riemannian submersions. We obtain characterizations, investigate the geometry
of foliations which arise from the definition of this new submersion. After we
investigate the geometry of foliations, we obtain necessary and sufficient
condition for base manifold to be a locally product manifold and proving new
conditions to be totally umbilical and totally geodesicness, respectively.
Moreover, some examples of such submersions are mentioned.
