We introduce the notion of CR quaternionic map and we prove that any such real analytic map, between CR quaternionic manifolds, is the restriction of a quaternionic map between quaternionic manifolds. As an application we prove, for example, that for any submanifold M, of dimension 4k-1, of a quaternionic manifold N, such that TM generates a quaternionic subbundle of TN restricted to M, of (real) rank 4k, there exists, locally, a quaternionic submanifold of N, containing M as a hypersurface.
A note on CR-quaternionic maps / Marchiafava, Stefano; R., Pantilie. - In: ADVANCES IN GEOMETRY. - ISSN 1615-715X. - STAMPA. - 13:(2013), pp. -605--612. [10.1515/advgeom-2013-0006]