TY - JOUR
ID - 1671
TI - Some rigidity results on complete Finsler manifolds
JO - Journal of Finsler Geometry and its Applications
JA - JFGA
LA - en
SN -
AU - Asanjarani, Azam
AU - R. Dehkordi, Hengameh
AD - Department of Statistics, The University of Auckland, Auckland, New Zealand
AD - Center of Mathematics, Computing and Cognition - CMCC
Federal University of ABC - UFABC, SP, Brazil.
Y1 - 2022
PY - 2022
VL - 3
IS - 1
SP - 100
EP - 117
KW - Finsler metric
KW - Rigidity
KW - Constant curvature
KW - Second-order differential equation
KW - Adapted coordinate
DO - 10.22098/jfga.2022.10415.1061
N2 - We provide an extension of Obata's theorem to Finsler geometry and establish some rigidity results based on a second-order differential equation. Mainly, we prove that every complete simply connected Finsler manifold of positive constant flag curvature is isometrically homeomorphic to a Euclidean sphere endowed with a certain Finsler metric and vice versa. Based on these results, we present a classification of Finsler manifolds which admit a transnormal function. Specifically, we show that if a complete Finsler manifold admits a transnormal function with exactly two critical points, then it is homeomorphic to a sphere.
UR - https://jfga.uma.ac.ir/article_1671.html
L1 - https://jfga.uma.ac.ir/article_1671_16df84e3513a82e16e6237882007ccd7.pdf
ER -