Torsion of α-connections on the density manifold

Publikationstyp
Conference Paper
Date Issued
2025-10
Sprache
English
Author(s)
Ay, Nihat 
Data Science Foundations E-21  
Schwachhöfer, Lorenz  
TORE-URI
https://hdl.handle.net/11420/58936
First published in
Lecture notes in computer science  
Number in series
16035
Start Page
417
End Page
427
Citation
7th International Conference on Geometric Science of Information, GSI 2025
Contribution to Conference
7th International Conference on Geometric Science of Information, GSI 2025  
Publisher DOI
10.1007/978-3-032-03924-8_43
Publisher
Springer
ISBN of container
978-3-032-03924-8
978-3-032-03923-1
We study the torsion of the α-connections defined on the density manifold in terms of a regular Riemannian metric. In the case of the Fisher-Rao metric our results confirm the fact that all α-connections are torsion free. For the α-connections ∇(O,α) obtained by the Otto metric, we show that, except for α=−1, they are not torsion free and that ∇(O,0) is compatible with the Otto metric, but not its Levi-Civita connection. In fact, we derive an explicit formula for this torsion and show that the ∇(O,0)-geodesics differ from those of the Otto metric.
Subjects
Otto metric
Fisher-Rao metric
Wasserstein geometry
α-connections
DDC Class
005.7: Data