Open AccessAffine functions and Busemann functions on complete Finsler manifolds
Author(s) -
Nobuhiro Innami,
Yoe Itokawa,
Tetsuya Nagano,
Katsuhiro Shiohama
Publication year - 2021
Publication title -
proceedings of the american mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.968
H-Index - 84
eISSN - 1088-6826
pISSN - 0002-9939
DOI - 10.1090/proc/15304
Subject(s) - affine transformation , minkowski space , mathematics , manifold (fluid mechanics) , pure mathematics , dimension (graph theory) , finsler manifold , affine coordinate system , space (punctuation) , function (biology) , relation (database) , mathematical analysis , affine space , computer science , geometry , curvature , ricci curvature , mechanical engineering , evolutionary biology , biology , engineering , operating system , database
We clarify the relation between an affine function and a Busemann function in a geodesically complete Finsler manifold. As an application, we give the characterization of a Minkowski space by means of the dimension of the vector space consisting of all affine functions on a Finsler manifold.