Complex and Lagrangian surfaces of the complex projective plane via Kählerian Killing Spin c spinors - Nakad, Roger; Roth, Julien (Journal of geometry and physics, 2017)
The complex projective space CP 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 Lagrangian or complex surface M 2 characterizes the isometric immersion of M into CP 2 .