Resumen de Linearizability of d-webs, d ≥ 4, on two-dimensional manifolds

Maks A. Akivis, Vladislav V. Goldberg, Valentin V. Lychagin

• 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 g4(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 g4, and d − 4 PDEs of the second order with respect to f and g4,..., 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.