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Moscow Mathematical Journal, 2003, Volume 3, Number 2, Pages 681–690
DOI: https://doi.org/10.17323/1609-4514-2003-3-2-681-690 (Mi mmj105) 		 
This article is cited in 10 scientific papers (total in 10 papers)

On skew loops, skew branes and quadratic hypersurfaces

S. L. Tabachnikov

Department of Mathematics, Pennsylvania State University
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DOI: https://doi.org/10.17323/1609-4514-2003-3-2-681-690
Abstract: A skew brane is an immersed codimension 2 submanifold in affine space, free from pairs of parallel tangent spaces. Using Morse theory, we prove that a skew brane cannot lie on a quadratic hypersurface. We also prove that there are no skew loops on embedded ruled developable discs in 3-space.
Key words and phrases: Skew loops and skew branes, quadratic hypersurfaces, double normals, Morse theory, developable surfaces.
Bibliographic databases:
MSC: 53A05, 53C50, 58E05
Language: English
Citation: S. L. Tabachnikov, “On skew loops, skew branes and quadratic hypersurfaces”, Mosc. Math. J., 3:2 (2003), 681–690
Citation in format AMSBIB
\Bibitem{Tab03}
\by S.~L.~Tabachnikov
\paper On skew loops, skew branes and quadratic hypersurfaces
\jour Mosc. Math.~J.
\yr 2003
\vol 3
\issue 2
\pages 681--690
\mathnet{http://mi.mathnet.ru/mmj105}
\crossref{https://doi.org/10.17323/1609-4514-2003-3-2-681-690}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2025279}
\zmath{https://zbmath.org/?q=an:1050.53010}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=000208594200018}
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    • This publication is cited in the following 10 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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