Geodesic Webs and PDE Systems of Euler Equations
We find necessary and sufficient conditions for the foliation defined by level sets of a function f(x1, ..., xn) 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 + 1) 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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CitationActa Applicandae Mathematicae: An International Survey Journal on Applying Mathematics and Mathematical Applications DOI 10.1007/s10440-009-9437-1
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