A new look at adapted complex structures

Abstract

Given a closed real analytic Riemannian manifold, we construct and study a one parameter family of adapted complex structures on the manifold of its geodesics.

8 pages

References in corpus (5)

• Geometric quantization and the generalized Segal-Bargmann transform for Lie groups of compact type
• Cycle Spaces of Flag Domains: A Complex Geometric Viewpoint
• On the BKS pairing for Kahler quantizations of the cotangent bundle of a Lie group
• Geometric quantization, complex structures and the coherent state transform
• Adapted complex structures and the geodesic flow

Cited by in corpus (5)

• Complex structures adapted to magnetic flows
• Quantization of compact Riemannian symmetric spaces
• Complex symplectomorphisms and pseudo-Kähler islands in the quantization of toric manifolds
• On complexified analytic Hamiltonian flows and geodesics on the space of Kahler metrics
• Adapted complex and involutive structures