Results 1 to 10 of about 99 (87)

Certain Conditions for a Finsler Manifold to Be Isometric with a Finsler Sphere

Analysis and Geometry in Metric Spaces, 2022
We show that if there is a smooth function f on a Finsler n-space M satisfying Δ2f = −kfgΔf for a positive constant k, then M is diffeomorphic with the n-sphere 𝕊n, where g denotes the weighted Riemannian metric.
Yin Songting, Wang Huarong
exaly   +3 more sources

A Lichnerowicz–Obata–Cheng Type Theorem on Finsler Manifolds

Mathematics, 2018
Let ( M , F , d μ ) be a Finsler manifold with the Ricci curvature bounded below by a positive number and constant S-curvature. We prove that, if the first eigenvalue of the Finsler⁻Laplacian attains its lower bound, then M is ...
Pan Zhang, Yin Songting
exaly   +3 more sources

Closed Geodesics on Positively Curved Finsler 3-Spheres

Advanced Nonlinear Studies, 2016
Abstract In [33], Wang proved that for every Finsler three-dimensional sphere ( S 3
Huagui Duan
exaly   +3 more sources

Stability of closed geodesics on Finsler 2-spheres

Journal of Functional Analysis, 2008
The aim of the authors is to prove the following Theorem 2.1 On every Finsler 2-sphere with only finitely many prime geodesics, there exist always at least two irrationally elliptic prime geodesics. Their proof contains four ingredients: Morse theory, the precise index iteration formulae from [\textit{Y. Long}, Adv. Math. 154, No.~1, 76--131 (2000; Zbl
Yiming Long
exaly   +2 more sources

The existence of two closed geodesics on every Finsler 2-sphere [PDF]

Mathematische Annalen, 2009
36 pages, 1 figure, added a remark before Theorem 1 ...
Yiming Long, VÍCTOR Bangert, Long Yiming   +2 more
exaly   +5 more sources

Multiple closed geodesics on Finsler 3-dimensional sphere

Journal of Functional Analysis
In 1973, Katok constructed a non-degenerate (also called bumpy) Finsler metric on $S^3$ with exactly four prime closed geodesics. And then Anosov conjectured that four should be the optimal lower bound of the number of prime closed geodesics on every Finsler $S^3$. In this paper, we proved this conjecture for bumpy Finsler $S^{3}$ if the Morse index of
Huagui Duan
exaly   +4 more sources

Weighted Ricci curvature in Riemann-Finsler geometry [PDF]

AUT Journal of Mathematics and Computing, 2021
Ricci curvature is one of the important geometric quantities in Riemann-Finsler geometry. Together with the $S$-curvature, one can define a weighted Ricci curvature for a pair of Finsler metric and a volume form on a manifold.
Zhongmin Shen
doaj   +1 more source

The isoparametric functions on a class of Finsler spheres

Differential Geometry and its Applications, 2022
In this paper, we give global expressions of geodesics and isoparametric functions on a Randers sphere by navigation. We obtain isoparametric families and focal submanifolds in (S^{n}; F; dμ_{BH}) by Cartan-Münzner polynomials. Further more, we construct some examples of closed and non-closed geodesics, isoparametric functions, isoparametric families ...
Chen, Yali, He, Qun
openaire   +3 more sources

DEFORMATIONS OF THE VERONESE EMBEDDING AND FINSLER -SPHERES OF CONSTANT CURVATURE [PDF]

Journal of the Institute of Mathematics of Jussieu, 2021
AbstractWe establish a one-to-one correspondence between, on the one hand, Finsler structures on the $2$ -sphere with constant curvature $1$ and all geodesics closed, and on the other hand, Weyl connections on certain spindle orbifolds whose symmetric Ricci curvature is positive definite and whose geodesics are all closed. As an application of our
Christian Lange, Thomas Mettler
openaire   +6 more sources

Quantum Gravity Phenomenology Induced in the Propagation of UHECR, a Kinematical Solution in Finsler and Generalized Finsler Spacetime

Galaxies, 2021
It is well-known that the universe is opaque to the propagation of Ultra-High-Energy Cosmic Rays (UHECRs) since these particles dissipate energy during their propagation interacting with the background fields present in the universe, mainly with the ...
Marco Danilo Claudio Torri
doaj   +1 more source