The geometry of a 3-quasi-Sasakian manifold

Abstract

3-quasi-Sasakian manifolds were studied systematically by the authors in a recent paper as a suitable setting unifying 3-Sasakian and 3-cosymplectic geometries. In this paper many geometric properties of this class of almost 3-contact metric manifolds are found. In particular, it is proved that the only 3-quasi-Sasakian manifolds of rank 4l+1 are the 3-cosymplectic manifolds and any 3-quasi-Sasakian manifold of maximal rank is necessarily 3-á-Sasakian. Furthermore, the transverse geometry of a 3-quasi-Sasakian manifold is studied, proving that any 3-quasi- Sasakian manifold admits a canonical transversal, projectable quaternionic-K¨ahler structure and a canonical transversal, projectable 3-á-Sasakian structure.