Abstract
A generalization of holomorphic forms on Riemann surfaces to higher-dimensional manifolds with a spin-structure (so called monogenic forms) is described. Monogenic forms on R m were defined by Delanghe, Sommen and Soucek in recently published monograph on Clifford analysis. In the paper, the definition is generalized to the curved case (i.e. to manifolds with a spin-structure). Monogenic forms of any degree are defined in such a way that monogenic 0-forms are harmonic spinors, i.e. solutions of the Dirac equation. An analogue of the Cauchy theorem is proved for monogenic forms.
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