PROPERTIES OF SADDLE SURFACES OF GALILEAN SPACE
Keywords:
Galilean space, degenerate metric, motion, Gaussian curvature, cyclic, saddle, transfer surface, rotations, singular plane, curvature defect, asymptotic directionAbstract
The saddle surfaces of the Galilean space, which are a space with a degenerate metric, are studied in this paper. The surfaces of rotation are investigated, and the surface curvature defect is proved to be zero. The class of surfaces of rotation of constant curvature is defined.
The saddle surfaces of the Galilean space were studied and they are divided into two types: “saddle” and “cyclic saddle”. It is proved that there is no movement of Galilean space transforming a surface of one type into another. An example of a saddle surface of various types, which are equal in Euclidean space, is given. The saddle transfer surfaces were studied.
References
А.Артыкбоев., Д.Д.Соколов. Геометрия в целом в пространстве-время “ Т.: Фан. 1991. 179 с. (Geometry as a whole in space-time)
A.Artykbayev, B.M.Sultanov/ Invariants of surface indicatrix in a Special linear transformation. Mathematics and statistics. USA 7(4):106-115.2019
A.Artykbayev, B.M.Sultanov Research of parabolic surface points in Galilean space. Bulletin of National University of Uzbekistan: Mathematics and Natural Sciences.
Розенфельд Б.А. Многомерные пространства. М.: Наука. Главная редакция физико-математической литературы, 1966.-648 с.: ил.
Э.К.Курбонов О поверхности галилеева пространства. Узбекский математический журнал, № 1, 46–52 (2005).( On the surface of the Galilean space)
U.Ozturk, E.B.Koc Ozturk, E.Nesovic. On eqiform Darboux helices in Galilean 3-space. Math. Commun. 23(2018), 145–159.
M.Dede, C. Ekici, W.Geomans Surface of revalution with vanishing curvature in Galilean 3-space/ Journal of Mathematical Physics, Analysis, Geometry.Vol.14 issue 2,141-152 (2018).
Э.Г. Позняк, Е.В. Шикин. Дифференциалная геометрия Московского университета 1990 курси. (Differential geometry)
Яглом И. М. Принцип относительности галилеевой и неевклидовой геометрии. Наука, Москва, (1969). - 394 ст, (Relativity principle of Galilean and non-Euclidean geometry)
Султанов Б.М. Поверхности, определяемые символами Кристоффеля. Современные проблемы геометрии и топологии и ее приложения. 21-23 ноября, Ташкент, Узбекистан, 2019. pp 180-181.( Surfaces defined by Christoffel symbols).
