In Riemannian geometry, the **sectional curvature** is one of the ways to describe the curvature of Riemannian manifolds. The sectional curvature *K*(σ_{p}) depends on a two-dimensional plane σ_{p} in the tangent space at *p*. It is the Gaussian curvature of the surface which has the plane σ_{p} as a tangent plane at *p*, obtained from geodesics which start at *p* in the directions of σ_{p} (in other words, the image of σ_{p} 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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