4-Webs in the Plane and their Linearizability

Document Type

Article

Publication Date

1-1-2004

Abstract

We investigate the linearizability problem for different classes of 4-webs in the plane In particular, we apply the linearizability conditions, recently found by Akivis, Goldberg and Lychagin, to confirm that a 4-web MW (Mayrhofer's web) with equal curvature forms of its 3-subwebs and a nonconstant basic invariant is always linearizable (this result was first obtained by Mayrhofer in 1928; it also follows from the papers of Nakai) Using the same conditions, we further prove that such a 4-web with a constant basic invariant (Nakai's web) is linearizable if and only if it is parallelizable. Next we study four classes of the so-called almost parallelizable 4-webs APWa, a = 1, 2, 3, 4 (for them the curvature K = 0 and the basic invariant is constant on the leaves of the web foliation Xa), and prove that a 4-web APW a is linearizable if and only if it coincides with a 4-web MW a of the corresponding special class of 4-webs MW The existence theorems are proved for all the classes of 4-webs considered in the paper.

Identifier

1342281372 (Scopus)

Publication Title

Acta Applicandae Mathematicae

External Full Text Location

https://doi.org/10.1023/B:ACAP.0000013251.38211.88

ISSN

01678019

First Page

35

Last Page

55

Issue

1

Volume

80

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