X-Nico

Differential topology

Differential topology also deals with questions like these, which specifically pertain to the properties of differentiable mappings on Rⁿ (for example the tangent bundle, jet bundles, the Whitney extension theorem, and so forth).

see also

Curvature of Riemannian manifolds

The curvature of n-dimensional Riemannian manifold is given by an antisymmetric n×n matrix $\backslash Omega^\{\}\; \{\}=\backslash Omega^i\; \{\backslash \; j\}$ of 2-forms (or equivalently a 2-form with values in $so(n)$, the Lie algebra of the orthogonal group $O(n)$, which is the structure group of the tangent bundle of a Riemannian manifold).