http://de.evo-art.org/index.php?action=history&feed=atom&title=Girl%27s_Surface 2026-05-17T16:46:02Z Versionsgeschichte dieser Seite in de_evolutionary_art_org MediaWiki 1.27.4 http://de.evo-art.org/index.php?title=Girl%27s_Surface&diff=3927&oldid=prev 2015-01-28T14:51:07Z

<p>Die Seite wurde neu angelegt: „ == Reference == Sue Goodman, Alex Mellnik and Carlo H. Séquin: <a href="/index.php?title=Girl%27s_Surface" title="Girl's Surface">Girl&#039;s Surface</a>. In: <a href="/index.php?title=Bridges_2013" title="Bridges 2013">Bridges 2013</a>. Pages 383–388 == DOI == == Abstract == Boy’s…“</p> <p><b>Neue Seite</b></p><div><br /> <br /> == Reference ==<br /> Sue Goodman, Alex Mellnik and Carlo H. Séquin: [[Girl&#039;s Surface]]. In: [[Bridges 2013]]. Pages 383–388 <br /> <br /> == DOI ==<br /> <br /> == Abstract ==<br /> Boy’s surface is the simplest and most symmetrical way of making a compact model of the projective plane in R3<br /> without any singular points. This surface has 3-fold rotational symmetry and a single triple point from which three<br /> loops of intersection lines emerge. It turns out that there is a second, homeomorphically different way to model the<br /> projective plane with the same set of intersection lines, though it is less symmetrical. There seems to be only one<br /> such other structure beside Boy’s surface, and it thus has been named Girl’s surface. This alternative, finite, smooth<br /> model of the projective plane seems to be virtually unknown, and the purpose of this paper is to introduce it and<br /> make it understandable to a much wider audience. To do so, we will focus on the construction of the most<br /> symmetrical Möbius band with a circular boundary and with an internal surface patch with the intersection line<br /> structure specified above. This geometry defines a Girl’s cap with C2 front-to-back symmetry.<br /> <br /> == Extended Abstract ==<br /> <br /> == Bibtex == <br /> <br /> == Used References ==<br /> [1] F. Apéry, Models of the Real Projective Plane. (Braunschweig: Vieweg, 1987).<br /> <br /> [2] T. F. Banchoff, Triple points and surgery of immersed surfaces. Proc. Amer. Math. Soc. (1974), pp 407-413.<br /> <br /> [3] W. Boy, Über die Curvatura integra und die Topologie geschlossener Flächen. Math. Ann. 57 (1903), pp 151-184.<br /> <br /> [4] S. Goodman and M. Kossowski, Immersions of the projective plane with one triple point. Differential Geom. Appl. 27 (2009).<br /> <br /> [5] G. Howard and S. Goodman, Generic maps of the projective plane with a single triple point. Math. Proc. Cambridge Phil. Soc, 152 (2012), pp 455-472.<br /> <br /> [6] S. Izumiya and W. L. Marar, The Euler characteristic of a generic wavefront in a 3-manifold. Proc. Amer. Math. Soc. (1993), 1347–1350.<br /> <br /> [7] A. Mellnik, Two immersions of the projective plane. – http://surfaces.gotfork.net/<br /> <br /> [8] U. Pinkall, Regular Homotopy classes of immersed surfaces. Topology 24 (1985), pp 421-434.<br /> <br /> [9] H. Samelson, Orientability of hypersurfaces in Rn. Proc. Amer. Math. Soc. (1969), pp 301–302.<br /> <br /> [10] C. H. Séquin, Cross-Caps - Boy Caps - Boy Cups. Bridges Conf., July 26-31, 2013.<br /> <br /> <br /> == Links ==<br /> === Full Text === <br /> http://archive.bridgesmathart.org/2013/bridges2013-383.pdf<br /> <br /> [[intern file]]<br /> <br /> === Sonstige Links ===<br /> http://archive.bridgesmathart.org/2013/bridges2013-383.html</div>

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