Geodesic Webs on a Two-Dimensional Manifold and Euler Equations

Details Geodesic Webs on a Two-Dimensional Manifold and Euler Equations Geodesic Webs on a Two-Dimensional Manifold and Euler Equations

2008-10-30

arxiv.org/abs/0810.5392v1

Mathematics

Differential Geometry

15 pages

Scientific paper

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 also find conditions for the projective structure mentioned above to contain an affine symmetric connection, and conditions for a planar 4-web to be equivalent to a geodesic 4-web on an affine symmetric surface. Similar results are obtained for planar d-webs, d > 4, provided that additional d-4 second-order invariants vanish.

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