title: Quaternionic-like manifolds and homogeneous twistor spaces.
abstract: Motivated by the quaternionic geometry corresponding to the homogeneous complex manifolds endowed with (holomorphically) embedded spheres, we introduce and initiate the study of the 'quaternionic-like manifolds'. These contain, as particular subclasses, the CR quaternionic and theρ-quaternionic manifolds. Moreover, the notion of 'heaven space' finds its adequate level of generality in this setting: (essentially) any real analytic quaternionic-like manifold admits a (germ) unique heaven space, which is aρ-quaternionic manifold. We, also, give a natural construction of homogeneous complex manifolds endowed with embedded spheres, thus, emphasizing the abundance of the quaternionic-like manifolds.
authors.affiliation: Institutul de Matematică 'Simion Stoilow' al Academiei Române , C.P. 1-764, 014700, Bucureşti, România.
authors.forename: Radu
authors.identifier: 0000-0002-4693-025X
authors.initials: R
authors.lastname: Pantilie
keywords: embeddings of the Riemann sphere; quaternionic geometry; twistor theory