Abstract
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 resolves the Blaschke conjecture for 3-webs. We also give the algorithm for determining whether a given 3-web is linearizable, find the linearity condition for 3-webs and establish its relationships to the condition that a plane curve consists of flexes and to the Euler equation in gas-dynamics.
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Goldberg, V.V., Lychagin, V.V. On the Blaschke conjecture for 3-webs. J Geom Anal 16, 69–115 (2006). https://doi.org/10.1007/BF02930988
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DOI: https://doi.org/10.1007/BF02930988