Almost CR quaternionic manifolds and their immersibility in HP^n

Abstract

We apply the general theory of codimension one integrability conditions for $G$-structures developed in arXiv:1306.6817v3 [math.DG] to the case of quaternionic CR geometry. We obtain necessary and sufficient conditions for an almost CR quaternionic manifold to admit local immersions as an hypersurface of the quaternionic projective space. We construct a deformation of the standard quaternionic contact structure on the quaternionic Heisenberg group which does not admit local immersions in any quaternionic manifold.

24 pages, v3: improved presentation v4: final version to appear in Abh. Math. Semin. Univ. Hambg

References in corpus (2)

• Twistor Theory for CR quaternionic manifolds and related structures
• A generalized integrability problem for G-Structures

Cited by in corpus (1)

• A generalized integrability problem for G-Structures