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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.
Gauss's Theorema Egregium (Latin for "Remarkable Theorem") is a major result of differential geometry, ... (G. I. Taylor Lecture) on YouTube, 30 January 2023 ...
In differential geometry, the two principal curvatures at a given point of a surface are the maximum and minimum values of the curvature as expressed by the eigenvalues of the shape operator at that point. They measure how the surface bends by different amounts in different directions at that point.
The classical nineteenth century approach to the differential geometry of surfaces, due in large part to Carl Friedrich Gauss, has been reworked in this modern framework, which provides the natural setting for the classical theory of the moving frame as well as the Riemannian geometry of higher-dimensional Riemannian manifolds.
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).
See also multivariable calculus, list of multivariable calculus topics. Manifold. Differentiable manifold; Smooth manifold; Banach manifold; Fréchet manifold; Tensor analysis. Tangent vector
In differential geometry, the holonomy of a connection on a smooth manifold is the extent to which parallel transport around closed loops fails to preserve the geometrical data being transported. Holonomy is a general geometrical consequence of the curvature of the connection.
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.