On Clairaut semi-invariant Riemannian maps to Sasakian manifolds

Abstract

In this paper, we define Clairaut semi-invariant Riemannian maps to Sasakian manifolds. We obtain the necessary and sufficient conditions for a curve on a base manifold to be geodesic. We also find the conditions for semi-invaraint Riemannian maps to be Clairaut semiinvariant Riemannian map. Further, we calculate the necessary and sufficient conditions of these maps to be totally geodesic. Also, we discuss the biharmonicity condition of this map. Later on, we obtain the inequality results for these maps. Finally, we give non-trivial examples to show the existence of these maps.