Definition
Given a Riemannian manifold and two linearly independent tangent vectors at the same point, u and v, we can define
Here R is the Riemann curvature tensor.
In particular, if u and v are orthonormal, then
The sectional curvature in fact depends only on the 2-plane σp in the tangent space at p spanned by u and v. It is called the sectional curvature of the 2-plane σp, and is denoted K(σp).
Read more about this topic: Sectional Curvature
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