Two-dimensional geodesic flows having first integrals of higher degree

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Abstract

We present a family of riemannian metrics on two-sphere having the property that the geodesic flows admit first integrals which are fiberwise homogeneous polynomials of degree greater than 2. They also have the property that all geodesics are closed.

Original languageEnglish
Pages (from-to)487-505
Number of pages19
JournalMathematische Annalen
Volume320
Issue number3
DOIs
Publication statusPublished - 2001
Externally publishedYes

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ASJC Scopus subject areas

  • Mathematics(all)

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