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arXiv · 1708.01996

Projective invariants of linear 3-webs and Gronwall's Conjecture

Sergey I. Agafonov
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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.

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Sergey I. Agafonov. 2017-08-07. Projective invariants of linear 3-webs and Gronwall's Conjecture. https://arxiv.org/abs/1708.01996

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