# Finsler metric of scalar curvature

From Diffgeom

Template:Finsler metric property

## Definition

A Finsler metric on a differential manifold is said to be of **scalar curvature** if the flag curvature depends only on the point and nonzero vector chosen at that point, and *not* on the choice of tangent plane.

Equivalently, the flag curvature can be viewed as a function of the slit tangent bundle, where elements of the slit tangent bundle are orderd pairs of a pointand a nonzero vector at that point.