Ads
related to: elementary differential geometry
Search results
Results From The WOW.Com Content Network
e. Differential geometry is a mathematical discipline that studies the geometry of smooth shapes and smooth spaces, otherwise known as smooth manifolds. It uses the techniques of differential calculus, integral calculus, linear algebra and multilinear algebra. The field has its origins in the study of spherical geometry as far back as antiquity.
Differentiable curve. Differential geometry of curves is the branch of geometry that deals with smooth curves in the plane and the Euclidean space by methods of differential and integral calculus . Many specific curves have been thoroughly investigated using the synthetic approach. Differential geometry takes another path: curves are ...
The Mercator projection preserves angles but fails to preserve area, hence the massive distortion of Antarctica. Gauss's Theorema Egregium (Latin for "Remarkable Theorem") is a major result of differential geometry, proved by Carl Friedrich Gauss in 1827, that concerns the curvature of surfaces. The theorem says that Gaussian curvature can be ...
Barrett O'Neill (1924– 16 June 2011) was an American mathematician. [1] He is known for contributions to differential geometry, including two widely-used textbooks on its foundational theory. [2] He was the author of eighteen research articles, the last of which was published in 1973.
Nevertheless, this suffices to develop an elementary and quite intuitive approach to calculus using infinitesimals, see transfer principle. Differential geometry. The notion of a differential motivates several concepts in differential geometry (and differential topology). The differential (Pushforward) of a map between manifolds.
In differential geometry, the Atiyah–Singer index theorem, proved by Michael Atiyah and Isadore Singer (1963), [1] states that for an elliptic differential operator on a compact manifold, the analytical index (related to the dimension of the space of solutions) is equal to the topological index (defined in terms of some topological data).
Ads
related to: elementary differential geometry