Pseudoholomorphicity of Closed Minimal Surfaces in Constantly Curved 4-Spaces

Chi-Ming Yau
1990 Proceedings of the American Mathematical Society  
The twistor lifts of a minimal surface in a constantly curved 4-space are studied. Computing the Laplacian of the length of their differentials provides a topological condition for pseudoholomorphicity. Geometric conditions for holomorphicity of surfaces in flat spaces are found.
doi:10.2307/2047752 fatcat:w73r63ywdfejnh7t2ecfri4pa4