NDLI: 4-Webs in the Plane and Their Linearizability

Content Provider	Springer Nature Link
Author	Goldberg, Vladislav V.
Copyright Year	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 APW a ,a=1,2,3,4 (for them the curvature K=0 and the basic invariant is constant on the leaves of the web foliation X a ), 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.
Starting Page	35
Ending Page	55
Page Count	21
File Format	PDF
ISSN	01678019
Journal	Acta Applicandae Mathematica
Volume Number	80
Issue Number	1
e-ISSN	15729036
Language	English
Publisher	Kluwer Academic Publishers
Publisher Date	2004-01-01
Publisher Place	Dordrecht
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Computer Science Mathematics Mathematical and Computational Physics Statistical Physics Mechanics
Content Type	Text
Resource Type	Article
Subject	Applied Mathematics

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