As we have seen, by introducing the notion of curvature tensor K ∇, with any pair of tangent vectors Y, Z ∈ T x M we associated a linear transformation K x (Y, Z) of the tangent space T x M. Let F x be an oriented plane spanned by Y, Z (that is, Y, Z are basis vectors in F x .) Let S F be a surface (in M) generated by geodesics tangent to F, more precisely, if U is a sufficiently small neighborhood in F x , then the exponential mapping U → exp x (U) =: S F is a diffeomorphism and the inner product in T x M induces a non-degenerate inner product in any tangent plane T x S F . Thus, the so obtained manifold S F is Riemannian and one can talk about its Gauss curvature \( {K_S}_{_F} = :K\left( {x,F} \right) \equiv {K_x}\left( F \right) \) called the sectional curvature in bi-direction F.