  Normality equations describe Newtonian dynamical systems admitting normal
shift of hypersurfaces. They were first derived in Euclidean geometry, then in
Riemannian geometry. Recently they were rederived in more general case, when
geometry of manifold is given by generalized Legendre transformation. As
appears, in this case some part of normality equations describe generalized
Legendre transformation itself irrespective to that Newtonian dynamical system,
for which others are written. In present paper this smaller part of normality
equations is studied.
