# differential geometry

## English

### Noun

differential geometry (usually uncountable, plural differential geometries)

1. (geometry, 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.