differential geometry

differential geometry (usually uncountable, plural differential geometries)

1. (geometry, mathematical analysis) The study of geometry, especially geometric structures on differentiable manifolds, using techniques from calculus, linear algebra and multilinear algebra.
   • 1945, Eric Temple Bell, The Development of Mathematics, 2nd Edition, 1992 Republication, page 358,

     […] projective differential geometries of the American and Italian schools do not seem to have attracted physicists.

   • 1962, I. M. James, The Mathematical Works of J. H. C. Whitehead, Volume 1: Differential Geometry, page 189,

     The general theory of manifolds of class 2 is a sub-class of differential geometries, which contain the theory of affine connections, curvature and osculating sub-spaces.

   • 1993, M. A. Akivis, V. V. Goldberg, Projective Differential Geometry of Submanifolds, page v:

     Note that projective differential geometry is a basis for Euclidean and non-Euclidean differential geometries since metric properties of submanifolds of Euclidean and non-Euclidean spaces should only be added to their projective properties.

   • 2012, Heinrich W. Guggenheimer, Differential Geometry, page 145:

     In this sense, ${\displaystyle C^{k_{0}}}$ is the natural hypothesis of differentiability in the particular question of differential geometry.

• algebraic geometry
• analytic geometry
• projective geometry