structural:reformatting, structural:scholar_edition
Differentiable curve

Roughly speaking a differentiable curve is a curve that is defined as being locally the image of an injective differentiable function γ: I → X {\displaystyle \gamma \colon I\rightarrow X} from an interval I of the real numbers into a differentiable manifold X, often R n. {\displaystyle \mathbb {R} ^{n}.}

More precisely, a differentiable curve is a subset C of X where every point of C has a neighborhood U such that C ∩ U {\displaystyle C\cap U} is diffeomorphic to an interval of the real numbers. In other words, a differentiable curve is a differentiable manifold of dimension one.