We apply the general theory of codimension one integrability conditions for G-structures developed in Santi (Ann Mat Pura Appl 195:1463–1489, 2016) 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.
SANTI, A. (2017). Almost CR quaternionic manifolds and their immersibility in HP^n. ABHANDLUNGEN AUS DEM MATHEMATISCHEN SEMINAR DER UNIVERSITAT HAMBURG, 87, 83-103 [10.1007/s12188-016-0136-3].
Almost CR quaternionic manifolds and their immersibility in HP^n
SANTI, ANDREA
2017
Abstract
We apply the general theory of codimension one integrability conditions for G-structures developed in Santi (Ann Mat Pura Appl 195:1463–1489, 2016) 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.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
