Monge-Ampère equation, hyperkähler structure and adapted complex structure

Su-Jen Kan

In the tangent bundle of $(M,g)$, it is well-known that the Monge-Ampère equation $(\partial \bar{\partial }\sqrt{\rho }{)}^n=0$ has the asymptotic expansion $ ρ(x+iy)=\sum_{ij} g_{ij} (x) y_…