On the Blaschke conjecture for 3-webs
Abstract
We find relative differential invariants of orders eight and nine for a planar nonparallelizable 3-web such that their vanishing is necessary and sufficient for a 3-web to be linearizable. This solves the Blaschke conjecture for 3-webs. As a side result, we show that the number of linearizations in the Gronwall conjecture does not exceed fifteen and give criteria for rigidity of 3-webs.
- Publication:
-
arXiv Mathematics e-prints
- Pub Date:
- November 2004
- DOI:
- arXiv:
- arXiv:math/0411460
- Bibcode:
- 2004math.....11460G
- Keywords:
-
- Mathematics - Differential Geometry;
- 53A60
- E-Print:
- LaTeX, 52 pages