Open AccessDeformation of one-sided surfaces
Author(s) -
М. А. Чешкова
Publication year - 2021
Publication title -
differencialʹnaâ geometriâ mnogoobrazij figur
Language(s) - English
Resource type - Journals
eISSN - 2782-3229
pISSN - 0321-4796
DOI - 10.5922/0321-4796-2020-52-14
Subject(s) - klein bottle , surface (topology) , bottle , deformation (meteorology) , geometry , plane (geometry) , point (geometry) , mathematics , projective plane , projective test , projective geometry , physics , materials science , pure mathematics , composite material , differential geometry , torus , correlation
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.