Complexified diffeomorphism groups, totally real submanifolds and Kähler–Einstein geometry
Complexified diffeomorphism groups, totally real submanifolds and Kähler–Einstein geometry
Let (M,J) be an almost complex manifold. We show that the infinite-dimensional space Tau of totally real submanifolds in M carries a natural connection. This induces a canonical notion of geodesics in Tau and a corresponding definition of when a functional, defined on Tau, is convex. Geodesics in Tau can …