The Differential of the Exponential Map for Reductive Homogeneous Spaces

Key Points

• This research aims to extend Helgason's formula to apply it within the context of reductive homogeneous spaces and manifolds that possess torsion-free affine connections.
• Generalized Helgason's formula for Taylor series
• Applied technique to reductive homogeneous spaces
• Included manifolds with torsion-free affine connections
• Establishes a new mathematical framework for the exponential map
• Demonstrates relationships applicable beyond symmetric spaces
• Provides a foundation for further studies in geometry and topology