Geodesic Webs and PDE Systems of Euler Equations

2008/10/30 by Vladislav V. Goldberg, Goldberg, Vladislav V., Valentin V. Lychagin +1
Mathematics · #53A60 #Differential Geometry (math.DG) #FOS: Mathematics #math.DG #msc:53A60

paper · pdf · doi:10.48550/arxiv.0810.5417

9 pages

arxiv created 2008/10/30 · arxiv updated 2009/12/01

Abstract

We find necessary and sufficient conditions for the foliation defined by level sets of a function f(x₁,...,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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