# affine connection in a sentence

- Curvature and torsion are the main invariants of an
*affine connection*. - On any manifold of positive dimension there are infinitely many
*affine connections*. - Much like
*affine connections*, projective connections also define geodesics. - Given an arbitrary linear connection \ Gamma on TX, the corresponding
*affine connection* - There are different physical interpretations of the translation part \ Theta of
*affine connections*. - It's difficult to find
*affine connection* in a sentence. - The
*affine connection* may be used for defining torsion, like is usual in Riemannian geometry. - Although he initially assumed a symmetric
*affine connection*, like Einstein he later considered the nonsymmetric field. - However, this approach does not explain the geometry behind
*affine connections* nor how they acquired their name. - To take the metric and
*affine connection* as independent variables in the action principle was first considered by Palatini. - This extension of the notion of affine spaces to manifolds in general is developed in the article on the
*affine connection*. - An
*affine connection* is called complete if the exponential map is well-defined at every point of the tangent bundle. - The main invariants of an
*affine connection* are its Lie bracket of vector fields can be recovered from the affine connection. - The main invariants of an affine connection are its Lie bracket of vector fields can be recovered from the
*affine connection*. - The curvature tensor can also be defined for any pseudo-Riemannian manifold, or indeed any manifold equipped with an
*affine connection*. - A basic result of differential geometry states that normal coordinates at a point always exist on a manifold with a symmetric
*affine connection*.