differential geometry

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differential geometry

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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