Hypergeometric functions and the ultrahyperbolic Dirac operator

Abstract

In this article, we realize a projective model for the equivalent of the unit sphere S m−1⊂ℝ m in the orthogonal space ℝ p, q of ultrahyperbolic signature (p, q), and we define a Dirac operator on this surface within the context of the Clifford analysis. We then construct null solutions of a special type for this operator, hence obtaining a relationship between hypergeometric functions and spin-invariant systems.