Physical and Mathematical Sciences | Article | Published 2021
In the paper, we study some properties of convex surfaces in an isotropic space $R_3^2.$ The definitions of $R_3^2,$ the first and second quadratic forms of the surface are given, and an analogue of the sphere of the Euclidean space is found. The sphere of an isotropic space is a paraboloid of revolution. It is proved that the intersection of the sphere of an isotropic space is always an ellipse. The definition of the dual image of a plane with respect to the sphere of an isotropic space is given. Using the dual image, the generalized surface mapping is defined. Some properties of the dual surface are proved.