Product theorems on anti-invariant Riemannian submersions

Abstract

In Ali and Fatima (J Tensor Soc 6(2):163–175, 2012) we studied anti-invariant and Langrangian Riemannian submersions from nearly kaehler manifolds. In this paper we have continued the study of such submersion and investigate the geometry of the leaves of two distributions and obtain the necessary and sufficient conditions for a Langrangian Riemannian submersions to be totally geodesic map. In the end, the decomposition theorems for the total manifold of the submersion are obtained.