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Abstract
The classical web geometry [1,3,4] studies invariants of foliation families with respect to pseudogroup of diffeomorphisms. Thus for the case of planar 3-webs the basic semi invariant is the Blaschke curvature, [2]. It is also curvature of the Chern connection [4] that are naturally associated with a planar 3-web.
In this paper we investigate invariants of planar 3-webs with respect to group of symplectic diffeomorphisms. We found the basic symplectic invariants of planar 3-webs that allow us to solve the symplectic equivalence problem for planar 3-webs in general position. The Lie-Tresse theorem, [4], gives the complete description of the field of rational symplectic differential invariants of planar 3-webs. We also give normal forms for homogeneous 3-webs, i.e. 3-webs having constant basic invariants.
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References
2. Wilhelm Blaschke. Einfuhrung in die Geometrie der Waben. Birkhauser Verlag, Basel-Stuttgart, 1955.
3. Wilhelm Blaschke, Gerrit Bol. Geometrie der Gewebe. Topologische Fragen der Differentialgeometrie. J. W. Edwards, Ann Arbor, Michigan, 1944.
4. Shiing Shen Chern. Web geometry. Bull. Amer. Math. Soc. (N.S.), 6(1):1-8, 1982, doi: http://dx.doi.org/10.1090/S0273-0979-1982-14955-2.
5. Boris Kruglikov, Valentin Lychagin. Global Lie-Tresse theorem, volume 22. 2016, doi: http://dx.doi.org/10.1007/s00029-015-0220-z