No abstract

In a general and nonmetrical framework, we introduce the class of CR quaternionic manifolds containing the class of quaternionic manifolds, whilst in dimension three it particularizes to, essentially, give the conformal manifolds. We show that these manifolds have a rich natural Twistor Theory and, along the way, we obtain a heaven space construction for quaternionic manifolds. © 2011 Springer-Verlag

In a general and non metrical framework, we introduce the class of co-CR quaternionic manifolds, which contains the class of quaternionic manifolds, whilst in dimension three it particularizes to give the Einstein-Weyl spaces. We show that these manifolds have a rich natural Twistor Theory and, along the way, we obtain a heaven space construction for quaternionic-Kähler manifolds.

Abstract. On an almost quaternionic manifold (M 4n , Q) we study the integrability of almost complex structures which are compatible with the almost quaternionic structure Q. If n ≥ 2, we prove that the existence of two compatible complex structuresis an oriented conformal 4-manifold, we prove a maximum principle for the angle function I 1 , I 2 of two compatible complex structures and deduce an application to anti-self-dual manifolds.By considering the special class of Oproiu connections we prove the existence of a well defined almost complex structure J on the twistor space Z of an almost quaternionic manifold (M 4n , Q) and show that J is a complex structure if and only if Q is quaternionic. This is a natural generalization of the Penrose twistor constructions.

Quaternion generalized fiber bundles {Mathematical expression} are studied, both isomorphic to global tensorial product {Mathematical expression} ordinary quaternion fiber bundles right and left respectively) and quite general ones. A cohomology class {Mathematical expression} is considered which represents the obstruction in order the fiber bundle be a tensorial product. Several properties and a splitting principle are proved for bundles {Mathematical expression}. On this ground and founding on a convenient bundle BE → X associated to jaz (that we call Bonan's bundle and for which e{open}( {Mathematical expression}=e{open}(BE)) relations are stated among Stiefel-Whitney classes of {Mathematical expression}, BE and the class e{open}. © 1975 Fondazione Annali di Matematica Pura ed Applicata