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.
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.
Reference
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