1307.0493 (Daniel Burns et al.)

The exponential map of the complexification of {\em Ham} in the
real-analytic case    [PDF]

Daniel Burns, Ernesto Lupercio, Alejandro Uribe

Let $(M, \omega, J)$ be a K\"ahler manifold and K its group of hamiltonian symplectomorphisms. The complexification of K introduced by Donadson is not a group, only a "formal Lie group". However it still makes sense to talk about the exponential map in the complexification. In this note we show how to construct geometrically the exponential map (for small time), in case the initial data are real-analytic. The construction is motivated by, but does not use, semiclassical analysis.

View original: http://arxiv.org/abs/1307.0493