Browsing by Subject "math.DG"
Now showing items 1-2 of 2
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First integrals of affine connections and Hamiltonian systems of hydrodynamic type
(Oxford University PressJournal of Integrable Systems, 2016-12-23)We find necessary and sufficient conditions for a local geodesic flow of an affine connection on a surface to admit a linear first integral. The conditions are expressed in terms of two scalar invariants of differential ...
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The geodesic X-ray transform with a $GL(n,\mathbb{C})$-connection
We derive reconstruction formulas for a family of geodesic ray transforms with connection, defined on simple Riemannian surfaces. Such formulas provide injectivity of such all transforms in a neighbourhood of constant ...