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math.DG2024
Cartan-Schouten metrics for information geometry and machine learning
Andre Diatta, Bakary Manga, Fatimata Sy
We study Cartan-Schouten metrics, explore invariant dual connections, and propose them as models for Information Geometry. Based on the underlying Riemannian barycenter and the bii…
math.DG2023
On dual quaternions, dual split quaternions and Cartan-Schouten metrics on perfect Lie groups
Andre Diatta, Bakary Manga, Fatimata Sy
We discuss Cartan-Schouten metrics (Riemannian or pseudo-Riemannian metrics that are parallel with respect to the Cartan-Schouten canonical connection) on perfect Lie groups. Appli…