Linearizability of d-webs, d ≥ 4, on two-dimensional manifolds
Permanent lenke
https://hdl.handle.net/10037/2056Dato
2004-03-31Type
Journal articleTidsskriftartikkel
Peer reviewed
Sammendrag
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), ..., gd(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, ..., gd. For d = 4, this result confirms
Blaschke’s conjecture on the nature of conditions for the linearizabilty
of a 4-web. We also give Mathematica codes for testing 4- and d-webs
(d > 4) for linearizability and examples of their usage.
Beskrivelse
Dette er forfatternes aksepterte versjon.
Forlag
Birkhäuser BaselSitering
Akivis, M.A., Goldberg, V.V. & Lychagin, V.V. Linearizability of d-webs, d ≥ 4, on two-dimensional manifolds. Sel. math., New ser. 10, 431 (2005).Metadata
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