Pseudoholomorphicity of closed minimal surfaces in constantly curved 4-spaces

Yau, Chi-Ming

doi:10.1090/S0002-9939-1990-1030738-0

Pseudoholomorphicity of closed minimal surfaces in constantly curved $4$-spaces
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Proc. Amer. Math. Soc. 110 (1990), 1027-1032 Request permission

Abstract:

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.

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