Fundamental theorem of curves

In differential geometry, the fundamental theorem of space curves states that every regular curve in three-dimensional space, with non-zero curvature, has its shape (and size or scale) completely determined by its curvature and torsion.[1][2]

  1. ^ Banchoff, Thomas F.; Lovett, Stephen T. (2010), Differential Geometry of Curves and Surfaces, CRC Press, p. 84, ISBN 9781568814568.
  2. ^ Agricola, Ilka; Friedrich, Thomas (2002), Global Analysis: Differential Forms in Analysis, Geometry, and Physics, Graduate Studies in Mathematics, vol. 52, American Mathematical Society, p. 133, ISBN 9780821829516.