Closed geodesics on orbifolds of revolution

• Autores: J. Borzellino, C. Jordan-Squire, D. Mark Sullivan, Gregory C. Petrics
• Localización: Houston journal of mathematics, ISSN 0362-1588, Vol. 33, Nº 4, 2007, págs. 1011-1025
• Idioma: inglés
• Texto completo no disponible (Saber más ...)
• Resumen

  • Using the theory of geodesics on surfaces of revolution, we show that any two-dimensional orbifold of revolution homeomorphic to S2 must contain an infinite number of geometrically distinct closed geodesics. Since any such orbifold of revolution can be regarded as a topological two-sphere with metric singularities, we will have extended Bangert's theorem on the existence of infinitely many closed geodesics on any smooth Riemannian two-sphere. In addition, we give an example of a two-sphere cone-manifold of revolution which possesses a single closed geodesic, thus showing that Bangert's result does not hold in the wider class of closed surfaces with cone manifold structures.