Premium
On the Flag Curvature of Finsler Metrics of Scalar Curvature
Author(s) -
Chen Xinyue,
Mo Xiaohuan,
Shen Zhongmin
Publication year - 2003
Publication title -
journal of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.441
H-Index - 62
eISSN - 1469-7750
pISSN - 0024-6107
DOI - 10.1112/s0024610703004599
Subject(s) - scalar curvature , curvature , mathematics , sectional curvature , finsler manifold , curvature form , flag (linear algebra) , isotropy , mathematical analysis , prescribed scalar curvature problem , torsion (gastropod) , pure mathematics , geometry , physics , algebra over a field , medicine , surgery , quantum mechanics
The flag curvature of a Finsler metric is called a Riemannian quantity because it is an extension of sectional curvature in Riemannian geometry. In Finsler geometry, there are several non‐Riemannian quantities such as the (mean) Cartan torsion, the (mean) Landsberg curvature and the S‐curvature, which all vanish for Riemannian metrics. It is important to understand the geometric meanings of these quantities. In the paper, Finsler metrics of scalar curvature (that is, the flag curvature is a scalar function on the slit tangent bundle) are studied and the flag curvature is partially determined when certain non‐Riemannian quantities are isotropic. Using the obtained formula for the flag curvature, locally projectively flat Randers metrics with isotropic S‐curvature are classified.