Finsler metric of scalar curvature

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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.