NORMAL VECTORS OF EUCLIDEAN MULTIDIMENSIONAL SURFACES 

Dolgarev Artur Ivanovich, Candidate of physical and mathematical sciences, associate professor, sub-department of mathematics and supercomputer modeling, Penza State University (40 Krasnaya street, Penza, Russia), deiivar@yandex.ru

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10.21685/2072-3040-2016-4-7

Background. Surfaces of multidimensional Euclidean spaces are actively investigated nowadays. One distinguishes hypersurfaces and cylindrical surfaces. In many cases there is a need for vectors of surface normal. The surface, described by several explicit scalar functions of multiple parameters, is an intersection of cylindrical surfaces. Therefore, there is a need for methods to obtain normals of cylindrical surfaces.
Materials and methods. Normal vectors of cylindrical surfaces appear to be ad multivectos, and the properties of cylindrical surfaces are used in the study of intersection surfaces.
Results. The author obtained coordinates of normal vectors of cylindrical surfaces. It has been established that normal planes of surfaces are generated by normal vectors of cylindrical surfaces. Ad exemplum, the researcher found coordinates of normal vectors of the Veronese surface of the 8D Euclidean space, set by 5 scalar functions, and gave the surface’s normal plane.
Conclusions. The author has obtained normal planes of surfaces of multidimensional Euclidean spaces.

multidimensional Euclidean space, surface, cylindrical surface, coordinates of normal vectors, normal plane surfaces, metric form of a surface, surface determinability 

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