Projective invariants of linear 3-webs and Gronwall's Conjecture
Differential Geometry
2019-03-05 v2
Abstract
We present a projectively invariant description of planar linear 3-webs. For a non-hexagonal 3-web, we introduce family of projective torsion-free Cartan connections, the web leaves being geodesics for each member of the family, and give a web linearization criterion. Finally, we propose an algorithm for resolving the Gronwall conjecture and illustrate this approach by proving the conjecture for 3-webs whose 2 foliations are 2 pencils of lines.
Keywords
Cite
@article{arxiv.1708.01996,
title = {Projective invariants of linear 3-webs and Gronwall's Conjecture},
author = {Sergey I. Agafonov},
journal= {arXiv preprint arXiv:1708.01996},
year = {2019}
}
Comments
The previous versions have a crucial computational error, making the construction of "counterexamples" invalid