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| 1 | Point |
| 1 | Vector Subspace |
| 2 | Surface |
| 3 | Span |
| 4 | Riemannian Metric |
| 9 | Gaussian Curvature |
| 13 | Riemann Curvature Tensor |
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Sectional Curvature
Let 
be a Riemannian manifold. Let 
be a point
in 
and let 
be a two-dimensional subspace
of 
. Then the sectional curvature of 
at 
is defined as
span
, 
is the metric tensor
and 
is the Riemann's curvature tensor.
This is a natural generalization of the classical Gaussian curvature for surfaces.