  As a generalization of holomorphic submersions, anti-invariant submersions
and slant submersions, we introduce slant Riemannian maps from almost Hermitian
manifolds to Riemannian manifolds. We give examples, obtain the existence
conditions of slant Riemannian maps and investigate harmonicity of such maps.
We also obtain necessary and sufficient conditions for slant Riemannian maps to
be totally geodesic and give a decomposition theorem for the total manifold.
