Differential invariants of webs on two-dimensional manifolds. (English. Russian original) Zbl 0714.53019
Math. Notes 48, No. 1, 639-647 (1990); translation from Mat. Zametki 48, No. 1, 26-37 (1990).
An n-web of curves on a two-dimensional manifold appears naturally as a web of characteristic curves of a hyperbolic system of differential equations of first order with two independent variables. For such a web scalar differential invariants are found. This allows the authors to find many properties of n-webs. In particular, they find some new necessary and sufficient conditions for an n-web to be parallelizable.
Remarks: The authors use the term “linear” instead of “parallelizable”. However, in web theory an n-web is linear it it is equivalent to an n-web consisting of n families of straight lines, and it is parallelizable if the straight lines of each of the families indicated above are parallel.]
Remarks: The authors use the term “linear” instead of “parallelizable”. However, in web theory an n-web is linear it it is equivalent to an n-web consisting of n families of straight lines, and it is parallelizable if the straight lines of each of the families indicated above are parallel.]
Reviewer: V.V.Goldberg
MSC:
| 53A60 | Differential geometry of webs |
Keywords:
hyperbolic system of differential equations; scalar differential invariants; n-webs; parallelizableReferences:
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