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math.DG2008★ 1 cited
Geodesic Webs and PDE Systems of Euler Equations
Vladislav V. Goldberg, Valentin V. Lychagin
We find necessary and sufficient conditions for the foliation defined by level sets of a function f(x_{1},...,x_{n}) to be totally geodesic in a torsion-free connection and apply t…
math.DG2008★ 1 cited
Geodesic Webs on a Two-Dimensional Manifold and Euler Equations
Vladislav V. Goldberg, Valentin V. Lychagin
We prove that any planar 4-web defines a unique projective structure in the plane in such a way that the leaves of the foliations are geodesics of this projective structure. We als…