Clairaut invariant Riemannian maps with Kähler structure

In this paper, we study Clairaut invariant Riemannian maps from Kähler manifolds to Riemannian manifolds, and from Riemannian manifolds to Kähler manifolds. We find necessary and sufficient conditions for the curves on the total spaces and base spaces of invariant Riemannian maps to be geodesic. Further, we obtain necessary and sufficient conditions for invariant Riemannian maps from Kähler manifolds to Riemannian manifolds to be Clairaut invariant Riemannian maps. Moreover, we obtain a necessary and sufficient condition for invariant Riemannian maps from Riemannian manifolds to Kähler manifolds to be Clairaut invariant Riemannian maps. We also give nontrivial examples of Clairaut invariant Riemannian maps whose total manifolds or base manifolds are Kähler manifolds

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