Loop space of a Kähler manifold

2025/01/27 by Anakkar, M.
#Complex Variables (math.CV) #Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2501.15984

Abstract

We prove that the loop space of a Kähler manifold inherits a Kähler structure. Then we prove that equipped with this natural metric the loop space is complete and unbounded. Additionally, we show that a geodesic on the loop space can be constructed by piecing together geodesics from each individual leaf.

Related

• Kähler structures on spaces of framed curves
• Geometric structures on loop and path spaces
• Constructing Smooth Loop Spaces
• The Geometry of Loop Spaces I: H^s-Riemannian Metrics
• The differential topology of loop spaces