  The first time that the connection between isometric immersion of surfaces
and solutions of the Dirac equation appeared in the literature was in the
seminal paper of Thomas Friedrich in 1998. In consequence of that, several
authors contributed to this topic hereafter, by obtaining the spinorial
representation of Spin manifolds with arbitrary dimension and also by
presenting a generalization of the Weierstrass representation map, for example.
All these results assume that the manifolds and bundles involved carry a Spin
structure, however this hypothesis is somehow restrictive, as for instance, if
we consider complex manifolds, it is more natural to consider SpinC structures.
There exist an alternative to adapt this result to SpinC manifolds, where the
idea is to use the left regular representation of a Clifford algebra in itself
to build the spinor bundles, but unlike the original works of Friedrich and
Morel, this representation is not irreducible. Thus, this paper aims to present
the spinorial representation of SpinC manifolds into Euclidian space with
arbitrary dimensions using spinors that came from an irreducible representation
of a complex Clifford algebra.
