Abstract
Abstract We introduce the notion of CR quaternionic map and we prove that any such realanalytic 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|M of (real) rank 4k, there exists, locally, a quaternionic submanifold of N containing M as a hypersurface.
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