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Toggle Differential geometry of curves and surfaces subsection. ... Print/export Download as PDF; Printable version; In other projects
A basic result of differential geometry states that normal coordinates at a point always exist on a manifold with a symmetric affine connection. In such coordinates the covariant derivative reduces to a partial derivative (at p only), and the geodesics through p are locally linear functions of t (the affine parameter).
Differential geometry finds applications throughout mathematics and the natural sciences. Most prominently the language of differential geometry was used by Albert Einstein in his theory of general relativity, and subsequently by physicists in the development of quantum field theory and the standard model of particle physics.
In mathematics, more specifically in differential geometry, the de Rham theorem says that the ring homomorphism from the de Rham cohomology to the singular cohomology given by integration is an isomorphism. The Poincaré lemma implies that the de Rham cohomology is the sheaf cohomology with the constant sheaf . Thus, for abstract reason, the de ...
Print/export Download as PDF; Printable version; In other projects Wikidata item; ... Slice theorem (differential geometry) T. Tait–Kneser theorem;
Differential geometry stubs (1 C, 115 P) Pages in category "Differential geometry" The following 200 pages are in this category, out of approximately 379 total.
Print/export Download as PDF; Printable version; In other projects ... Lectures on Classical Differential Geometry, Dover Publications, p. 108, ...
Defining the differential as a kind of differential form, specifically the exterior derivative of a function. The infinitesimal increments are then identified with vectors in the tangent space at a point. This approach is popular in differential geometry and related fields, because it readily generalizes to mappings between differentiable ...
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