A note on CR quaternionic maps

TL;DR

This paper introduces CR quaternionic maps, showing they extend to quaternionic maps, and applies this to demonstrate the local existence of quaternionic submanifolds containing certain hypersurfaces.

Contribution

It defines CR quaternionic maps and proves their extension to quaternionic maps, providing new insights into the structure of quaternionic submanifolds.

Findings

CR quaternionic maps extend to quaternionic maps

Existence of quaternionic submanifolds containing specified hypersurfaces

Extension results for submanifolds in quaternionic geometry

Abstract

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 $TN|_M$, of (real) rank $4k$, there exists, locally, a quaternionic submanifold of $N$, containing $M$ as a hypersurface.