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Closed geodesics on connected sums and 3-manifolds. / Rademacher, Hans Bert; Taimanov, Iskander A.
в: Journal of Differential Geometry, Том 120, № 3, 2022, стр. 557-573.Результаты исследований: Научные публикации в периодических изданиях › статья › Рецензирование
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TY - JOUR
T1 - Closed geodesics on connected sums and 3-manifolds
AU - Rademacher, Hans Bert
AU - Taimanov, Iskander A.
N1 - Publisher Copyright: © 2022 International Press of Boston, Inc.. All rights reserved.
PY - 2022
Y1 - 2022
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=85130106876&partnerID=8YFLogxK
U2 - 10.4310/JDG/1649953350
DO - 10.4310/JDG/1649953350
M3 - Article
AN - SCOPUS:85130106876
VL - 120
SP - 557
EP - 573
JO - Journal of Differential Geometry
JF - Journal of Differential Geometry
SN - 0022-040X
IS - 3
ER -
ID: 36167415