Affine manifold

In differential geometry, an affine manifold is a differentiable manifold equipped with a flat, torsion-free connection.

Equivalently, it is a manifold that is (if connected) covered by an open subset of ${\Bbb R}^n$ , with monodromy acting by affine transformations. This equivalence is an easy corollary of Cartan–Ambrose–Hicks theorem.

单词	Affine manifold
释义	Affine manifold 英语百科 Affine manifold In differential geometry, an affine manifold is a differentiable manifold equipped with a flat, torsion-free connection. Equivalently, it is a manifold that is (if connected) covered by an open subset of ${\Bbb R}^n$ , with monodromy acting by affine transformations. This equivalence is an easy corollary of Cartan–Ambrose–Hicks theorem.
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