Clairaut Anti-invariant Riemannian Maps from Kähler Manifolds

In this paper, we study Clairaut anti-invariant Riemannian map from a Kähler manifold to a Riemannian manifold and give non-trivial examples of such Riemannian maps. We obtain a necessary and sufficient condition for an anti-invariant Riemannian map to be Clairaut anti-invariant Riemannian map. Further, we establish curvature relations for total manifold and range F ∗ under Clairaut Lagrangian Riemannian map. We also obtain necessary and sufficient condition for vertical space ker F ∗ and horizontal space ( ker F ∗ ) ⊥ to define totally geodesic foliation on the total manifold.