Nets in Weyl spaces and their metrically equipped subspaces (Q2755665)

Let \(W_n\) be an \(n\)-dimensional Weyl space and let \(W_m\) be an \(m\)-dimensional submanifold in \(W_n\) equipped by a normal \(n-m\)-plane \(R_{n-m}\). The authors establish a correspondence between nets belonging to \(W_m\) and \(W_n\), find relations between the coefficients of the derivative equations of the fields of directions of the corresponding nets, construct the apparatus for studying the connection between the properties of of the corresponding nets, and investigate the properties of a net in \(W_n\) corresponding spacial nets of \(W_m\) such as Chebyshev's net of the first kind or the geodesic net or the \(c\)-net. The latter results generalize the results obtained in [\textit{S. A. Uysal} and \textit{A. Özdeger}, J. Geom. 51, 172-174; (1994; Zbl 0813.53035)].