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math.DG2026
Curvature Decomposition for Riemannian Lie Algebroids
René Langøen
Classical curvature formulas for Lie groups and Riemannian submersions are recast in terms of Lie groupoids with right-invariant source-fibre metrics and Riemannian Lie algebroids.…
math.DG2025
Curvature of Measure-Preserving Diffeomorphism Groups of Non-Orientable Surfaces
Boris Khesin, René Langøen, Irina Markina
We study curvatures of the groups of measure-preserving diffeomorphisms of non-orientable compact surfaces. For the cases of the Klein bottle and the real projective plane we compu…