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In this paper, we study the geometry of anti-invariant Riemanniansubmersions from a Kahler manifold onto a Riemannian manifold. Wefirst determine the base space when the total space of ananti-invariant Riemannian submersion is Einstein and then weinvestigate new conditions for anti-invariant Riemannian submersionsto be Clairaut submersions. We also focus on the geometry ofClairaut anti-invariant submersions.

EINSTEIN CONDITIONS FOR THE BASE SPACE OF ANTI-INVARIANT RIEMANNIAN SUBMERSIONS AND CLAIRAUT SUBMERSIONS