|
| | | | |
| | | |
| Stat |
Members: 3645
Articles: 2'506'133
Articles rated: 2609
26 April 2024 |
|
| | | | |
|
Article overview
| |
|
|
On affine hypersurfaces with everywhere nondegenerate Second Quadratic Form | | A. Khovanskii
; D. Novikov
; | | Date: |
19 Mar 2002 | | Subject: | Differential Geometry; Classical Analysis and ODEs MSC-class: 52A30;26B25,52A37 | math.DG math.CA | | Abstract: | 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. | | Source: | arXiv, math.DG/0203202 | | Services: | Forum | Review | PDF | Favorites | |
|
|
No review found.
Did you like this article?
Note: answers to reviews or questions about the article must be posted in the forum section.
Authors are not allowed to review their own article. They can use the forum section.
browser Mozilla/5.0 AppleWebKit/537.36 (KHTML, like Gecko; compatible; ClaudeBot/1.0; +claudebot@anthropic.com)
|
| |
|
|
|
|
News, job offers and information for researchers and scientists:
| |
REGISTER