Ay, NihatNihatAySchwachhöfer, LorenzLorenzSchwachhöfer2025-11-192025-11-192025-107th International Conference on Geometric Science of Information, GSI 2025https://hdl.handle.net/11420/58936We 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.enOtto metricFisher-Rao metricWasserstein geometryα-connectionsComputer Science, Information and General Works::005: Computer Programming, Programs, Data and Security::005.7: DataConference Paper10.1007/978-3-032-03924-8_43Conference Paper