The exponential map of the complexification of \em Ham in the real-analytic case

2013/07/01 by D. Burns, Burns, Daniel, Ernesto Lupercio +3 · 2 citations
Mathematics · #37J05 #53C55 #81S10 #Advanced Algebra and Geometry #FOS: Mathematics #FOS: Physical sciences #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Mathematical Physics (math-ph) #Symplectic Geometry (math.SG)

paper · pdf · doi:10.48550/arxiv.1307.0493

openalex publication_date 2013/07/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let (M, ω, J) be a Kähler 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.

Citations

• Geometric quantization and multiplicities of group representations

Cited by

• On complexified analytic Hamiltonian flows and geodesics on the space of\n Kahler metrics
• A new approximation method for geodesics on the space of Kähler metrics using complexified symplectomorphisms and Gröbner Lie series

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