Back Boysche Fläche German Superficie de Boy Spanish Surface de Boy French Superficie di Boy Italian ボーイ・サーフェス Japanese Поверхность Боя Russian Boyjeva ploskev Slovenian Поверхня Боя Ukrainian
In geometry, Boy's surface is an immersion of the real projective plane in three-dimensional space. It was discovered in 1901 by the German mathematician Werner Boy, who had been tasked by his doctoral thesis advisor David Hilbert to prove that the projective plane could not be immersed in three-dimensional space.
Boy's surface was first parametrized explicitly by Bernard Morin in 1978.[1] Another parametrization was discovered by Rob Kusner and Robert Bryant.[2] Boy's surface is one of the two possible immersions of the real projective plane which have only a single triple point.[3]
Unlike the Roman surface and the cross-cap, it has no other singularities than self-intersections (that is, it has no pinch-points).
- ^ Morin, Bernard (13 November 1978). "Équations du retournement de la sphère" [Equations of the eversion of the sphere] (PDF). Comptes Rendus de l'Académie des Sciences. Série A (in French). 287: 879–882.
- ^ Kusner, Rob (1987). "Conformal geometry and complete minimal surfaces" (PDF). Bulletin of the American Mathematical Society. New Series. 17 (2): 291–295. doi:10.1090/S0273-0979-1987-15564-9..
- ^ Goodman, Sue; Marek Kossowski (2009). "Immersions of the projective plane with one triple point". Differential Geometry and Its Applications. 27 (4): 527–542. doi:10.1016/j.difgeo.2009.01.011. ISSN 0926-2245.