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arXiv · 1606.05983

Complex and Lagrangian surfaces of the complex projective plane via K\"ahlerian Killing Spin$^c$ spinors

Roger Nakad·Julien Roth
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Abstract

The complex projective space $\mathbb C P^2$ of complex dimension $2$ has a Spin$^c$ structure carrying K\"ahlerian Killing spinors. The restriction of one of these K\"ahlerian 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.

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Roger Nakad, Julien Roth. 2016-06-20. Complex and Lagrangian surfaces of the complex projective plane via K\"ahlerian Killing Spin$^c$ spinors. https://doi.org/10.1016/j.geomphys.2017.02.005

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