Anti-invariant Riemannian submersions from cosymplectic manifolds onto Riemannian manifolds

Abstract

We introduce anti-invariant Riemannian submersions from cosymplectic manifolds onto Riemannian manifolds. We survey main results of anti-invariant Riemannian submersions defined on cosymplectic manifolds. We investigate necessary and sufficient condition for an anti-invariant Riemannian submersion to be totally geodesic and harmonic. We give examples of anti-invariant submersions such that characteristic vector field xi is vertical or horizontal. Moreover we give decomposition theorems by using the existence of anti-invariant Riemannian submersions.