Projective invariants of linear 3-webs and Gronwall's Conjecture
classification
🧮 math.DG
keywords
conjecturewebsfamilygronwalllinearprojectivealgorithmapproach
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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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Cited by 1 Pith paper
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A step to Gronwall's conjecture
The paper exhibits an invariant called the characteristic for generic points on plane linear 3-webs such that a diffeomorphism preserving it between two webs is locally a homography.
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