On affine hypersurfaces with everywhere nondegenerate Second Quadratic Form

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dc.creatorKhovanskii, A.
dc.creatorNovikov, D.
dc.date2002-03-19
dc.date.accessioned2026-07-07T04:47:11Z
dc.date.available2026-07-07T04:47:11Z
dc.descriptionConsider a closed connected hypersurface in $\mathbb{R}^n$ with constant signature (k,l) of the second quadratic form, and approaching a quadratic cone at infinity. This hypersurface divides $\mathbb{R}^n$ into two pieces. We prove that one of them contains a k-dimensional subspace, and another contains a l-dimensional subspace, thus proving an affine version of Arnold hypothesis. We construct an example of a surface of negative curvature in $\mathbb{R}^3$ with slightly different asymptotical behavior for which the previous claim is wrong.
dc.description18pp
dc.identifierhttps://arxiv.org/abs/math/0203202
dc.identifierhttp://arxiv.org/abs/math/0203202
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/63609
dc.subjectDifferential Geometry
dc.subjectClassical Analysis and ODEs
dc.subject52A30;26B25,52A37
dc.titleOn affine hypersurfaces with everywhere nondegenerate Second Quadratic Form
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