On the flag curvature of Finsler metrics of scalar curvature

Details On the flag curvature of Finsler metrics of scalar curvature On the flag curvature of Finsler metrics of scalar curvature

2003-03-12

arxiv.org/abs/math/0303144v1

Mathematics

Differential Geometry

23 pages

Scientific paper

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 this paper, we study Finsler metrics of scalar curvature (i.e., the flag curvature is a scalar function on the slit tangent bundle) and partially determine the flag curvature when certain non-Riemannian quantities are isotropic. Using the obtained formula for the flag curvature, we classify locally projectively flat Randers metrics with isotropic S-curvature.

Affiliated with

Also associated with

No associations

Rating

On the flag curvature of Finsler metrics of scalar curvature does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with On the flag curvature of Finsler metrics of scalar curvature, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and On the flag curvature of Finsler metrics of scalar curvature will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-204731