# HOLOMORPHIC LEGENDRIAN CURVES IN CP AND SUPERMINIMAL SURFACES IN S4

@inproceedings{Alarcn2019HOLOMORPHICLC, title={HOLOMORPHIC LEGENDRIAN CURVES IN CP AND SUPERMINIMAL SURFACES IN S4}, author={A. Alarc{\'o}n and F. Forstneri{\vc} and F. L{\'a}russon}, year={2019} }

We obtain a Runge approximation theorem for holomorphic Legendrian curves and immersions in the complex projective 3-space CP, both from open and compact Riemann surfaces, and we prove that the space of Legendrian immersions from an open Riemann surface into CP is path connected. We also show that holomorphic Legendrian immersions from Riemann surfaces of finite genus and at most countably many ends, none of which are point ends, satisfy the Calabi-Yau property. Coupled with the Runge… Expand

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