Zobrazeno 1 - 10
of 82
pro vyhledávání: '"53C22, 58E10"'
Autor:
Rademacher, Hans-Bert
We show that for a generic Riemannian metric on a compact manifold of dimension $n\ge 3$ all geodesic loops based at a fixed point have no self-intersections. We also show that for an open and dense subset of the space of Riemannian metrics on an $n$
Externí odkaz:
http://arxiv.org/abs/2407.02905
Autor:
Sciaraffia, Luciano
We study the existence of minimal networks in the unit sphere $\mathbf{S}^d$ and the unit ball $\mathbf{B}^d$ of $\mathbf{R}^d$ endowed with Riemannian metrics close to the standard ones. We employ a finite-dimensional reduction method, modelled on t
Externí odkaz:
http://arxiv.org/abs/2401.13134
Autor:
Zagane, Abderrahim
Publikováno v:
International Journal of Maps in Mathematics,Volume 7, Issue 2, 2024, Pages:138-155
In this paper, we investigate some geodesics and $F$-geodesics problems on tangent bundle and on $\varphi$-unit tangent bundle $T^{\varphi}_{1}M$ equipped with the $\varphi$-Sasaki metric over para-K\"{a}hler-Norden manifold $(M^{2m}, \varphi, g)$.
Externí odkaz:
http://arxiv.org/abs/2309.01830
Autor:
Shelukhin, Egor, Zhang, Jun
We prove that if the $m$-th homotopy group for $m \geq 2$ of a closed manifold has non-trivial invariants or coinvariants under the action of the fundamental group, then there exist infinitely many geometrically distinct closed geodesics for a $C^4$-
Externí odkaz:
http://arxiv.org/abs/2307.13877
Autor:
Oliveira, Goncalo
Motivated by some conjectures originating in the Physics literature, we use Foscolo's construction of Ricci-flat Kahler metrics on K3 surfaces to locate, with high precision, several closed geodesics and compute their index (their length is also appr
Externí odkaz:
http://arxiv.org/abs/2302.08354
Autor:
Rademacher, Hans-Bert
In this short note we discuss upper bounds for the critical values of homology classes in the based and free loop space of manifolds carrying a Riemannian or Finsler metric of positive Ricci curvature. In particular it follows that a shortest closed
Externí odkaz:
http://arxiv.org/abs/2203.14051
Autor:
Rademacher, Hans-Bert
We show that for an open and dense set non-reversible Finsler metrics on a sphere of odd dimension $n=2m-1 \ge 3$ there is a second closed geodesic with Morse index $\le 4(m+2)(m-1)+2.$
Comment: 16 pages, revised version, to appear in "Calc.Var.
Comment: 16 pages, revised version, to appear in "Calc.Var.
Externí odkaz:
http://arxiv.org/abs/2203.07896
Autor:
Kwong, Kwok-Kun, Lee, Hojoo
We present an elementary criterion to show the length-minimizing property of geodesics for a large class of conformal metrics. In particular, we prove the length-minimizing property of level curves of harmonic functions and the length-minimizing prop
Externí odkaz:
http://arxiv.org/abs/2202.00942
Publikováno v:
Math. Zeit. 302 (2022), 629-640
For compact manifolds with infinite fundamental group we present sufficient topological or metric conditions ensuring the existence of two geometrically distinct closed geodesics. We also show how results about generic Riemannian metrics can be carri
Externí odkaz:
http://arxiv.org/abs/2011.01909
Autor:
Allais, Simon, Soethe, Tobias
In this article, we give multiple situations when having one or two geometrically distinct closed geodesics on a complete Riemannian cylinder $M\simeq S^1\times\mathbb{R}$ or a complete Riemannian plane $M\simeq\mathbb{R}^2$ leads to having infinitel
Externí odkaz:
http://arxiv.org/abs/2005.10546