Paraquaternionic CR-submanifolds

Abstract

Paraquaternionic structures, at first known as quaternionic structures of second kind, are due to P. Libermann. Their study parallels that of quaternionic manifolds, yet relies on the algebra of paraquaternionic numbers. The counterpart in odd dimension of a paraquaternionic structure was introduced in 2006 by S. Ianuş, R. Mazzocco and G.E. Vîlcu and is referred to as a mixed 3-structure. It appears in a natural way on lightlike hypersurfaces in paraquaternionic manifolds. In this paper we review basic results concerning several types of submanifolds and semi-Riemannian submersions of manifolds endowed with paraquaternionic and mixed 3-structures.