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Mosc. Math. J., 2006, Volume 6, Number 1, Pages 135–152 (Mi mmj240)  

This article is cited in 1 scientific paper (total in 1 paper)

On affine hypersurfaces with everywhere nondegenerate second quadratic form

A. G. Khovanskiia, D. Novikovb

a University of Toronto
b Weizmann Institute of Science

Abstract: An Arnold conjecture claims that a real projective hypersurface with second quadratic form of constant signature $(k,l)$ should separate two projective subspaces of dimension $k$ and $l$ correspondingly. We consider affine versions of the conjecture dealing with hypersurfaces approaching at infinity two shifted halves of a standard cone. We prove that if the halves intersect, then the hypersurface does separate two affine subspaces. In the case of non-intersecting half-cones we construct an example of a surface of negative curvature in $\mathbb R^3$ bounding a domain without a line inside.

Key words and phrases: Arnold conjecture, ($k$, $l$)-hyperbolic hypersurface, convex-concave set.

DOI: https://doi.org/10.17323/1609-4514-2006-6-1-135-152

Full text: http://www.ams.org/.../abst6-1-2006.html
References: PDF file   HTML file

Bibliographic databases:

MSC: 52A30, 53A15
Received: January 26, 2005
Language:

Citation: A. G. Khovanskii, D. Novikov, “On affine hypersurfaces with everywhere nondegenerate second quadratic form”, Mosc. Math. J., 6:1 (2006), 135–152

Citation in format AMSBIB
\Bibitem{KhoNov06}
\by A.~G.~Khovanskii, D.~Novikov
\paper On affine hypersurfaces with everywhere nondegenerate second quadratic form
\jour Mosc. Math.~J.
\yr 2006
\vol 6
\issue 1
\pages 135--152
\mathnet{http://mi.mathnet.ru/mmj240}
\crossref{https://doi.org/10.17323/1609-4514-2006-6-1-135-152}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2265952}
\zmath{https://zbmath.org/?q=an:1132.52010}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000208595700009}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. M. F. Prokhorova, “Problems of homeomorphism arising in the theory of grid generation”, Proc. Steklov Inst. Math. (Suppl.), 261, suppl. 1 (2008), S165–S182  mathnet  crossref  isi  elib
  • Moscow Mathematical Journal
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