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arXiv · 0810.5417

Geodesic Webs and PDE Systems of Euler Equations

Vladislav V. Goldberg·Valentin V. Lychagin
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Abstract

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 them to find the conditions for d-webs of hypersurfaces to be geodesic, and in the case of flat connections, for d-webs (d > n) of hypersurfaces to be hyperplanar webs. These conditions are systems of generalized Euler equations, and for flat connections we give an explicit construction of their solutions.

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Vladislav V. Goldberg, Valentin V. Lychagin. 2008-10-30. Geodesic Webs and PDE Systems of Euler Equations. https://arxiv.org/abs/0810.5417

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