Closed geodesics on connected sums and 3-manifolds

Standard

Closed geodesics on connected sums and 3-manifolds. / Rademacher, Hans Bert; Taimanov, Iskander A.

In: Journal of Differential Geometry, Vol. 120, No. 3, 2022, p. 557-573.

Research output: Contribution to journal › Article › peer-review

Harvard

Rademacher, HB & Taimanov, IA 2022, 'Closed geodesics on connected sums and 3-manifolds', Journal of Differential Geometry, vol. 120, no. 3, pp. 557-573. https://doi.org/10.4310/JDG/1649953350

APA

Rademacher, H. B., & Taimanov, I. A. (2022). Closed geodesics on connected sums and 3-manifolds. Journal of Differential Geometry, 120(3), 557-573. https://doi.org/10.4310/JDG/1649953350

Vancouver

Rademacher HB, Taimanov IA. Closed geodesics on connected sums and 3-manifolds. Journal of Differential Geometry. 2022;120(3):557-573. doi: 10.4310/JDG/1649953350

Author

Rademacher, Hans Bert ; Taimanov, Iskander A. / Closed geodesics on connected sums and 3-manifolds. In: Journal of Differential Geometry. 2022 ; Vol. 120, No. 3. pp. 557-573.

BibTeX

@article{bca7bd3956bb4c529f638b90026e8293,

title = "Closed geodesics on connected sums and 3-manifolds",

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 simply-connected manifold which is not homeomorphic to a sphere.",

author = "Rademacher, {Hans Bert} and Taimanov, {Iskander A.}",

year = "2022",

doi = "10.4310/JDG/1649953350",

language = "English",

volume = "120",

pages = "557--573",

journal = "Journal of Differential Geometry",

issn = "0022-040X",

publisher = "International Press of Boston, Inc.",

number = "3",

}

RIS

TY - JOUR

T1 - Closed geodesics on connected sums and 3-manifolds

AU - Rademacher, Hans Bert

AU - Taimanov, Iskander A.

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