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Diffgeom β

Flag curvature

Definition

The flag curvature of a Finsler manifold (M,F) (viz a differential manifold M endowed with a Finsler metric F) defines a scalar (real number) for the following input: a point on the manifold, a tangent plane at that point, and a nonzero vector in the tangent plane.

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When the Finsler metricis a Riemannian metric, the flag curvature depends only on the tangent plane and not on the nonzero vector. Further, it equals the sectional curvature of that tangent plane.