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The first time that the connection between isometric immersion of surfacesand solutions of the Dirac equation appeared in the literature was in theseminal paper of Thomas Friedrich in 1998. In consequence of that, severalauthors contributed to this topic hereafter, by obtaining the spinorialrepresentation of Spin manifolds with arbitrary dimension and also bypresenting a generalization of the Weierstrass representation map, for example.All these results assume that the manifolds and bundles involved carry a Spinstructure, however this hypothesis is somehow restrictive, as for instance, ifwe consider complex manifolds, it is more natural to consider SpinC structures.There exist an alternative to adapt this result to SpinC manifolds, where theidea is to use the left regular representation of a Clifford algebra in itselfto build the spinor bundles, but unlike the original works of Friedrich andMorel, this representation is not irreducible. Thus, this paper aims to presentthe spinorial representation of SpinC manifolds into Euclidian space witharbitrary dimensions using spinors that came from an irreducible representationof a complex Clifford algebra.

Immersion in Rn by Complex irreducible Spinors