This article is cited in 1 paper

A sufficient condition for global regularity of nets of curves in the Euclidean plane

È. R. Rozendorn


Abstract: Sufficient conditions are obtained for a net of lines in a plane given by
$$ \alpha\,dx^2+2\beta\,dx\,dy+\gamma\,dy^2=0,\qquad\alpha\gamma-\beta^2<0, $$
to be homeomorphic to the cartesian net (globally or in some region). These conditions are expressed in terms of the integral of the modulus of the second Chebyshev vector of the net. We consider separately the special case when the net is formed by the characteristics of a hyperbolic transformation.
Figures: 7.
Bibliography: 6 titles.

UDC: 513.838

MSC: 53A05

Received: 12.04.1974

 English version: Mathematics of the USSR-Sbornik, 1975, 25:1, 111–127

Bibliographic databases:

• 
•