# Immersion in Sn by complex spinors

## TL;DR

This paper extends the spinor and Dirac equation approach to study isometric immersions of submanifolds within SpinC-manifolds of constant curvature, broadening the geometric framework beyond traditional Spin-manifolds.

## Contribution

It introduces a novel analysis of submanifolds in SpinC-manifolds, generalizing previous methods used for Spin-manifolds of constant curvature.

## Key findings

- Established a spinor-based characterization for immersions in SpinC-manifolds.
- Generalized existing theories from Spin to SpinC contexts.
- Provided new insights into the geometry of submanifolds in SpinC-structures.

## Abstract

Since the first work of Thomas Friedrich showing that isometric immersions of Riemann surfaces are related to spinors and the Dirac equation, various works appeared generalizing this approach to more general Spin-manifolds, in particular the case of submanifolds of Spin-manifolds of constant curvature. In the present work we investigate the case of submanifolds of SpinC-manifolds of constant curvature.