Deformation of one-sided surfaces

Abstract

The work is devoted to the study of the deformation of one-sided sur­faces. Let a normal vector be drawn along a closed curve on the surface. If, when returning to the original point, the direction of the normal coin­cides with the original direction of the normal, then the surface is called two-sided. Otherwise, we have a one-sided surface. Unilateral surfaces include: crossed cap, Roman surface, Boya surface, Klein bottle. Roman surface, Boya surface and crossed hood are a model of the projective plane. It is proved that if the surface is a model of a Moebius strip, of a Klein bottle, of projective plane, then the surface deformation is a Moebius strip model, a Klein bottle model, projective plane model respectively. Using a mathematical package, graphs are built the surfaces under consideration.