Lines on the surface in the quasi-hiperbolic space 11^S1/3

Дифференциальная геометрия многообразий фигур

V.B. Tsyrenova¹ 

[1] Banzarov Buryat State University;

关键词: quasi-hyperbolic space;    absolute;    surface;    canonical frame;    invariants;    lines on the surface;    geodesic lines;    semi-chebyshev and chebyshev networks;   

DOI  :  10.5922/0321-4796-2020-51-14

来源: DOAJ

【 摘 要 】

Quasi-hyperbolic spaces are projective spaces with decaying abso­lute. This work is a continuation of the author's work [7], in which surfac­es in one of these spaces are examined by methods of external forms and a moving frame. The semi-Chebyshev and Chebyshev net­works of lines on the surface in quasi-hyperbolic space are considered. In this pa­per we use the definition of parallel transfer adopted in [6]. By analogy with Euclidean geometry, the semi-Chebyshev network of lines on the surface is the network in which the tangents to the lines of one family are carried parallel along the lines of another family. A Che­byshev network is a network in which tangents to the lines of each family are carried parallel along the lines of another family. We proved three theorems. In Theorem 1, we obtain a natural equa­tion for non-geodesic lines that are part of a conjugate semi-Chebyshev network on the surface so that tangents to lines of another family are transferred in parallel along them. In Theorem 2, the natural equation of non-geodesic lines in the Chebyshev network is obtained. In Theorem 3 we prove that conjugate Chebyshev networks, one family of which is nei­ther geodesic lines, nor Euclidean sections, exist on surfaces with the lati­tude of four functions of one argument.

【 授权许可】

Unknown