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math.DG2025
Conjugate points on Lie groups with left-invariant metrics
Alice Le Brigant, Leandro Lichtenfelz, Stephen C. Preston
We prove sufficient conditions for the existence of conjugate points along geodesics of a left-invariant metric on a Lie group, using a reformulation of the index form in terms of…
math.DG2025
Singular Sets of Riemannian Exponential Maps in Hydrodynamics
James Benn, Patrick Heslin, Leandro Lichtenfelz +1
We prove that the singular sets for the Lagrangian solution maps of the two-dimensional inviscid Euler and generalized surface quasi-geostrophic equations are Gaussian null sets. T…
math.DG2025
Ricci curvature for hydrodynamics on the sphere
Leandro Lichtenfelz, Klas Modin, Stephen C. Preston
The geometric description of incompressible hydrodynamics, as geodesic motion on the infinite-dimensional group of volume-preserving diffeomorphisms, enables notions of curvature i…