On the Blaschke conjecture for 3-webs

Details On the Blaschke conjecture for 3-webs On the Blaschke conjecture for 3-webs

2004-11-21

arxiv.org/abs/math/0411460v1

J. Geom. Anal., 16 (2006) no. 1, 69-115

Mathematics

Differential Geometry

LaTeX, 52 pages

Scientific paper

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.

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