Abstract
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.
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Aynur Uysal, S., Özdeğer, A. On the Chebyshev nets in a hypersurface of a Weyl space. J Geom 51, 172–177 (1994). https://doi.org/10.1007/BF01226866
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DOI: https://doi.org/10.1007/BF01226866