Complex and Lagrangian surfaces of the complex projective plane via Kählerian Killing Spin${}^c$ spinors

Abstract

The complex projective space $\mathbb{C}{P}^2$ of complex dimension $2$ has a Spin${}^c$ structure carrying Kählerian Killing spinors. The restriction of one of these Kählerian Killing spinors to a surface $M^2$ characterizes the isometric immersion of $M^2$ into $\mathbb{C}{P}^2$ if the immersion is either Lagrangian or complex.

18 pages