Analyticity of Riemannian Exponential Maps on Diff(T)

Key Points

• The aim is to explore the properties of exponential maps on a specific Lie group using Riemannian metrics.
• Analyzed Sobolev type right-invariant Riemannian metrics of order k on the Lie group of diffeomorphisms.
• Proved existence of analytic Fréchet charts centered at identity point.
• Each exponential map induces an analytic structure on the Lie group.
• The findings provide a framework for understanding geometric properties of these maps.