differential geometry
noun1
Geometry, Mathematical analysis, Mathematics, Sciences Usually 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.
2 more examples
- 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:
- 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:
- Related terms
- algebraic geometry, analytic geometry, projective geometry