doiSerbia

Anti-invariant Riemannian submersions from nearly Kaehler manifolds

Ali Shahid (Department of Mathematics, Aligarh Muslim University, Aligarh, India)
Fatima Tanveer (Department of Mathematics, Aligarh Muslim University, Aligarh, India)

We extend the notion of anti-invariant and Langrangian Riemannian submersion to the case when the total manifold is nearly Kaehler. We obtain the integrability conditions for the horizontal distribution while it is noted that the vertical distribution is always integrable. We also investigate the geometry of the foliations of the two distributions and obtain the necessary and sufficient condition for a Langrangian submersion to be totally geodesic. The decomposition theorems for the total manifold of the submersion are obtained.

Keywords: Anti-invariant Riemannian Submersions, Langrangian Riemannian Submersions, Integrability, Decomposition Theorems