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A beautiful solution to the problem of isometric immersions in $\mathbb{R}^n$using spinors was found by Bayard, Lawn and Roth. However to use spinors onemust assume that the manifold carries a $\mbox{Spin}$-structure and, especiallyfor complex manifolds where is more natural to consider$\mbox{Spin}^{\mathbb{C}}$-structures, this hypothesis is somewhat restrictive.In the present work we show how the above solution can be adapted to$\mbox{Spin}^{\mathbb{C}}$-structures.

Immersion in $\mathbb{R}^n$ by complex spinors