##
**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; parallelizable
PDF
BibTeX
XML
Cite

\textit{A. M. Vinogradov} and \textit{V. A. Yumaguzhin}, Math. Notes 48, No. 1, 639--647 (1990; Zbl 0714.53019); translation from Mat. Zametki 48, No. 1, 26--37 (1990)

Full Text:
DOI

### References:

[1] | A. M. Vinogradov, ?Geometry of differential equations, the secondary differential calculus and quantum field theory,? Izv. Vuzov. Mat., No. 1, 13-21 (1986). |

[2] | W. Blaschke, Introduction to the Geometry of Webs [Russian translation], Fizmatgiz, Moscow (1959). |

[3] | A. M. Vinogradov, I. S. Krasil’shchik, and V. V. Lychagin, Introduction to the Geometry of Nonlinear Differential Equations [in Russian], Nauka, Moscow (1986). · Zbl 0592.35002 |

[4] | A. M. Vinogradov, ?The category of nonlinear differential equations,?, in: Equations on Manifolds [in Russian], Izdat. Voronezh. Univ., Voronezh (1982), pp. 26-51. |

[5] | D. V. Alekseevskii, A. M. Vinogradov, and V. V. Lychagin, ?Basic ideas and concepts of differential geometry,? Itogi Nauki Tekh. Ser. Sovremen. Probl. Mat. Fundament. Napravlen.,28 (1988). · Zbl 0735.53001 |

This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.