On the Chebyshev nets in a hypersurface of a Weyl space

In [1], Zlatanov introduced the Chebyshev vector fields of the first and second kind and the geodesic vector fields for an n-dimensional net in the Weyl spaceW_n. After having defined, in [2], the Chebyshev and geodesic curvatures of the lines of an arbitrary net,the b-nets and the c-nets, Tsareva and Zlatanov studied, among other things, some properties of the Chebyshev nets. In this paper, we consider an n-dimensional net in the hypersurfaceW_n of the Weyl SpaceW_n+1 and study some properties of the Chebyshev vector fields of the first and second kind and the geodesic vector fields of this net. Finally, two theorems concerning the b-nets and c-nets inW_n are obtained.