Closed geodesics on connected sums and 3-manifolds Full article
| Journal |
Journal of Differential Geometry
ISSN: 0022-040X , E-ISSN: 1945-743X |
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| Output data | Year: 2022, Volume: 120, Number: 3, Pages: 557-573 Pages count : 17 DOI: 10.4310/jdg/1649953350 | ||||||
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Abstract:
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 simplyconnected manifold which is not homeomorphic to a sphere.
Cite:
Rademacher H.-B.
, Taimanov I.A.
Closed geodesics on connected sums and 3-manifolds
Journal of Differential Geometry. 2022. V.120. N3. P.557-573. DOI: 10.4310/jdg/1649953350 WOS Scopus РИНЦ OpenAlex
Closed geodesics on connected sums and 3-manifolds
Journal of Differential Geometry. 2022. V.120. N3. P.557-573. DOI: 10.4310/jdg/1649953350 WOS Scopus РИНЦ OpenAlex
Dates:
| Submitted: | Sep 12, 2018 |
| Accepted: | Jan 7, 2020 |
| Published online: | Apr 15, 2022 |
Identifiers:
| Web of science: | WOS:000789251200006 |
| Scopus: | 2-s2.0-85130106876 |
| Elibrary: | 48584841 |
| OpenAlex: | W2892237837 |