A characterization of shortest geodesics on surfaces

Any finite configuration of curves with minimal intersections on a surface is a configuration of shortest geodesics for some Riemannian metric on the surface. The metric can be chosen to make the lengths of these geodesics equal to the number of intersections along them.

Keywords

Surfaces, curves, geodesics, minimal intersections, metrics

Mathematical Subject Classification 2000

Primary: 53C22

Secondary: 53C42, 57R42

References

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Publication

Received: 8 January 2001

Accepted: 17 May 2001

Published: 2 June 2001

Authors

Max Neumann-Coto
Instituto de Matemáticas UNAM Ciudad Universitaria México D.F. 04510 México

Volume 1, issue 1 (2001)

Max Neumann-Coto