  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.
