Closed geodesics on connected sums and 3-manifolds

Hans Bert Rademacher, Iskander A. Taimanov

Результат исследования: Научные публикации в периодических изданияхстатьярецензирование


We study the asymptotics of the number N(t) of geometrically distinct closed geodesics of length ≤ t of a Riemannian or Finsler metric on a connected sum of two compact manifolds of dimension at least three with non-trivial fundamental groups, and apply the results to the prime decomposition of a three-manifold. In particular we show that the function N(t) grows at least like the prime numbers on a compact 3-manifold with infinite fundamental group. It follows that a generic Riemannian metric on a compact 3-manifold has infinitely many geometrically distinct closed geodesics. We also consider the case of a connected sum of a compact manifold with positive first Betti number and a simply-connected manifold which is not homeomorphic to a sphere.

Язык оригиналаанглийский
Страницы (с-по)557-573
Число страниц17
ЖурналJournal of Differential Geometry
Номер выпуска3
СостояниеОпубликовано - 2022

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