Chebyshev nets formed by Ricci curves in a 3-dimensional Weyl space

In this paper, Ricci curves in a 3-dimensional Weyl space W 3 ( g , T ) are defined and it is shown that any 3-dimensional Chebyshev net formed by the three families of Ricci curves in a W 3 ( g , T ) having a definite metric and Ricci tensors is either a geodesic net or it consists of a geodesic subnet the members of which have vanishing second curvatures. In the case of an indefinite Ricci tensor, only one of the members of the geodesic subnet under consideration has a vanishing second curvature.