• matematica sub-riemannian
• math
• complex
• complesso
• quaternioni
• quaternions
• contact
• geometry
• contatto
• geometria

In this thesis, one may find a generalization to the quaternionic case of the fact that strictly pseudoconvex domains in the complex n-dimensional space, with n greater than 1, admits a structure of a sub-Riemannian manifold induced by the tangent complex space and its Levi form.
We retrace the proof of the complex case, and then we provide the necessary notion in the quaternionic context. Following S. Alesker's 2003 paper we introduce and study strictly quaternionic pseudoconvex domains in the quaternionic n-dimensional space, and the associated quaternionic Levi form, which relation mimics the one in the complex case. We endow the boundary of strictly quaternionic pseudoconvex domains with a weakly quaternionic contact structure, as defined in D. Duchemin's 2006 paper, induced by the tangent quaternionic space. This structure, in return, provides the means to prove the bracket-generating property needed to obtain a sub-Riemannian manifolds on the boundary of strictly quaternionic pseudoconvex domains with enough regularity.