Suppose \((M,g)\) denotes a Riemannian manifold and \(p\in M\). Let \(\Pi\subseteq T_pM\) be a 2-dimensional subspace and \(\exp_p \colon V\to U\) diffeomorphic. Then the sectional curvature of \(\Pi\), denoted by \(\sec \Pi\), is the Gaussian curvature of \(S_\Pi=\exp_p (\Pi\cap V)\) with the metric induced form the embedding \(S_\Pi\subseteq M\).
If \(v,w\in \Pi\) is a basis of \(\Pi\). Then we also use the notation \(\sec (v,w)\) for \(\sec \Pi\).