differential geometry en · NOUN
Meanings
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(uncountable, usually) The study of geometry, especially geometric structures on differentiable manifolds, using techniques from calculus, linear algebra and multilinear algebra.
In this sense, C#123;k#95;0#125; is the natural hypothesis of differentiability in the particular question of differential geometry.
2012, Heinrich W. Guggenheimer, Differential Geometry, page 145:1945, 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.
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.
1993, M. A. Akivis, V. V. Goldberg, Projective Differential Geometry of Submanifolds, page v: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.
Forms
| Spelling | Features | Labels | Source |
|---|---|---|---|
| differential geometries | Number=Plur | lexicographic |
Relateds
algebraic geometry · projective geometry · analytic geometry
Translations (14)
mk диференција́лна геоме́трија (differential geometry) · ru дифференциальная геометрия (differential geometry) · hu differenciálgeometria (differential geometry) · de Differenzialgeometrie (differential geometry) · ro geometrie diferențială (differential geometry) · es geometría diferencial (differential geometry) · ja 微分幾何学 (differential geometry) · de Differentialgeometrie (differential geometry) · fr géométrie différentielle (differential geometry) · it geometria differenziale (differential geometry) · pl geometria różniczkowa (differential geometry) · fi differentiaaligeometria (differential geometry) · cmn 微分幾何 /微分几何 (differential geometry) · sh diferencijalna geometrija (differential geometry)