Mathematics and Statistics Vol. 8(3), pp. 306 - 310
DOI: 10.13189/ms.2020.080309
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The Indicatrix of the Surface in Four-Dimensional Galilean Space


Artykbaev Abdullaaziz 1, Nurbayev Abdurashid Ravshanovich 2,*
1 Railway Engineering Institute, Uzbekistan
2 Department of Geometry and Topology, National University of Uzbekistan, Uzbekistan

ABSTRACT

This article discusses geometric quantities associated with the concept of surfaces and the indicatrix of a surface in four-dimensional Galileo space. In this case, the second orderly line in the plane is presented as a surface indicatrix. It is shown that with the help of the Galileo space movement, the second orderly line can be brought to the canonical form. The movement in the Galileo space is radically different from the movement in the Euclidean space. Galileo movements include parallel movement, axis rotation, and sliding. Sliding gives deformation in the Euclidean space. The surface indicatrix is deformed by the Galileo movement. When the indicatrix is deformed, the surface will be deformed. In the classification of three-dimensional surface points in the four-dimensional Galileo phase, the classification of the indicatrix of the surface at this point was used. This shows the cyclic state of surface points other than Euclidean geometry. The geometric characteristics of surface curves were determined using the indicatrix test. It is determined what kind of geometrical meaning the identified properties have in the Euclidean phase. It is shown that the Galilean movement gives surface deformation in the Euclidean sense. Deformation of the surface is indicated by the fact that the Gaussian curvature remains unchanged.

KEYWORDS
Principal Curvatures, Deformation, Galilean Space, Special Plane, Sliding, Surface Classification, Total Curvature, Cyclic Surface

Cite This Paper in IEEE or APA Citation Styles
(a). IEEE Format:
[1] Artykbaev Abdullaaziz , Nurbayev Abdurashid Ravshanovich , "The Indicatrix of the Surface in Four-Dimensional Galilean Space," Mathematics and Statistics, Vol. 8, No. 3, pp. 306 - 310, 2020. DOI: 10.13189/ms.2020.080309.

(b). APA Format:
Artykbaev Abdullaaziz , Nurbayev Abdurashid Ravshanovich (2020). The Indicatrix of the Surface in Four-Dimensional Galilean Space. Mathematics and Statistics, 8(3), 306 - 310. DOI: 10.13189/ms.2020.080309.