Boy's surface

In geometry, Boy's surface is an immersion of the real projective plane in 3-dimensional space found by Werner Boy in 1901. He discovered it on assignment from David Hilbert to prove that the projective plane could not be immersed in 3-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.

[Morin_1978-1] 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_1987-2] 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..

[Goodman2009-3] 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.

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