In Riemannian geometry, the sectional curvature is one of the ways to describe the curvature of Riemannian manifolds. The sectional curvature K(σp) depends on a two-dimensional plane σp in the tangent space at p. It is the Gaussian curvature of the surface which has the plane σp as a tangent plane at p, obtained from geodesics which start at p in the directions of σp (in other words, the image of σp under the exponential map at p). The sectional curvature is a smooth real-valued function on the 2-Grassmannian bundle over the manifold.
The sectional curvature determines the curvature tensor completely.
Read more about Sectional Curvature: Definition, Manifolds With Constant Sectional Curvature, Toponogov's Theorem, Manifolds With Non-positive Sectional Curvature, Manifolds With Positive Sectional Curvature
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