Research of parabolic surface points in Galilean space

Abstract

The paper studies the surfaces of the Galilean space R1 3. First, we consider the geometry of the surface in a small neighborhood of a point on the surface. Basically, we studied the points of the surface where at least one of the principal curvature appeals to zero. Two classes of points are defined where at least one of the principal curvature is zero. These points are divided into two types, parabolic and especially parabolic. It is proved that these neighborhoods using the movement of space is impossible to move each other. A sweep of surfaces with parabolic and especially parabolic points is constructed. A geometric image of the cone sweep in Galilean space is given. In Galilean space, we consider surfaces that do not have special planes. A class of surfaces with no special tangent planes is defined. A geometric image of a cone sweep in Galilean space is given. In Galilean space, surfaces that do not have special planes are considered. A class of surfaces is defined that do not have special tangent planes. At the end of the article, a classification of surface points in Galilean space is given.