On affine hypersurfaces with everywhere nondegenerate Second Quadratic Form

Details On affine hypersurfaces with everywhere nondegenerate Second Quadratic Form On affine hypersurfaces with everywhere nondegenerate Second Quadratic Form

2002-03-19

arxiv.org/abs/math/0203202v1

Mathematics

Differential Geometry

18pp

Scientific paper

Consider 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.

Affiliated with

Also associated with

No associations

Rating

On affine hypersurfaces with everywhere nondegenerate Second Quadratic Form does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with On affine hypersurfaces with everywhere nondegenerate Second Quadratic Form, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and On affine hypersurfaces with everywhere nondegenerate Second Quadratic Form will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-620468