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On the geometry of the nets in the n-dimensional space of Weyl

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Abstract

Chebyshev and geodesic curvatures of the lines of an arbitrary net belonging to the n-dimensional space of Weyl Wn are introduced. Characteristics of the following special nets in Wn are found: strongly parallel, b-net, c-net and orthogonal (theorems 1.2, 1.3, 1.5, 1.6). Some properties of the Chebyshev nets, orthogonal b-nets and orthogonal c-nets, of the Chebyshev vectors of the second kind, of the orthogonal nets and nets containing Chebyshev subnets are established (theorems 1.1, 1.7, 1.8, 1.4). The fundamental formulae in the case of an orthogonal coordinate net are obtained. The spaces Wn containing one of the following special orthogonal nets — strongly parallel of the first kind, Chebyshev net of the second kind and b-net are defined.

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Authors and Affiliations

  1. University of Plovdiv “Paissii Hilendarski”, 24 Tsar Assen, 4000, Plovdiv, Bulgaria

    Bistra Tsareva & Georgi Zlatanov

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  1. Bistra Tsareva
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  2. Georgi Zlatanov
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Tsareva, B., Zlatanov, G. On the geometry of the nets in the n-dimensional space of Weyl. J Geom 38, 182–197 (1990). https://doi.org/10.1007/BF01222903

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  • DOI: https://doi.org/10.1007/BF01222903

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