Linearizability of d-webs, d ≥ 4, on two-dimensional manifolds |
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Authors: | Maks A Akivis Vladislav V Goldberg Valentin V Lychagin |
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Affiliation: | 1. Department of Mathematics, Jerusalem College of Technology–Machon Lev, Havaad Haleumi St., POB 16031, Jerusalem, 91160, Israel 2. Department of Mathematical Sciences, New Jersey Institute of Technology, University Heights, Newark, NJ, 07102, USA 3. Department of Mathematics, The University of Tromso, N-9037, Tromso, Norway
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Abstract: | We find d − 2 relative differential invariants for a d-web, d ≥ 4, on a two-dimensional manifold and prove that their vanishing is necessary and sufficient for a d-web to be linearizable. If one writes the above invariants in terms of web functions f(x, y) and g
4(x, y),..., g
d
(x, y), then necessary and sufficient conditions for the linearizabilty of a d-web are two PDEs of the fourth order with respect to f and g
4, and d − 4 PDEs of the second order with respect to f and g
4,..., g
d
. For d = 4, this result confirms Blaschke’s conjecture on the nature of conditions for the linearizabilty of a 4-web. We also give
the Mathematica codes for testing 4- and d-webs (d > 4) for linearizability and examples of their usage. |
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Keywords: | |
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