In differential geometry, a geodesic is a generalization of the notion of a line to curved spaces. Planes. In Euclidean geometry a plane is a flat, two-dimensional surface that extends infinitely; the definitions for other types of geometries are generalizations of that. Planes are used in many areas of geometry.

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.It also relates to astronomy, the geodesy …

Riemannian geometry is the branch of differential geometry that studies Riemannian manifolds, smooth manifolds with a Riemannian metric, i.e. with an inner product on the tangent space at each point that varies smoothly from point to point. This gives, in particular, local notions of angle, length of curves, surface area and volume.From those, some other global quantities …

Differential heat treatment (also called selective heat treatment or local heat treatment) is a technique used during heat treating to harden or soften certain areas of a steel object, creating a difference in hardness between these areas. ... which will affect the geometry of the blade. An inexperienced polisher can quickly ruin a blade by ...

Numerical methods for ordinary differential equations are methods used to find numerical approximations to the solutions of ordinary differential equations (ODEs). Their use is also known as "numerical integration", although this term can also refer to the computation of integrals.Many differential equations cannot be solved exactly. For practical purposes, however – such as in …

In mathematics, differential topology is the field dealing with the topological properties and smooth properties of smooth manifolds.In this sense differential topology is distinct from the closely related field of differential geometry, which concerns the geometric properties of smooth manifolds, including notions of size, distance, and rigid shape. By comparison differential …

Overview Phase space coordinates (p,q) and Hamiltonian H. Let (,) be a mechanical system with the configuration space and the smooth Lagrangian . Select a standard coordinate system (, ˙) on . The quantities (, ˙,) = / ˙ are called momenta. (Also generalized momenta, conjugate momenta, and canonical momenta).For a time instant , the Legendre transformation of is defined as the …

Grigori Yakovlevich Perelman (Russian: Григорий Яковлевич Перельман, IPA: [ɡrʲɪˈɡorʲɪj ˈjakəvlʲɪvʲɪtɕ pʲɪrʲɪlʲˈman] (); born 13 June 1966) is a Russian mathematician who is known for his contributions to the fields of geometric analysis, Riemannian geometry, and geometric topology.He is widely regarded as one of the greatest living mathematicians.

Pages in category "Differential geometry" The following 200 pages are in this category, out of approximately 376 total. This list may not reflect recent changes.

In mathematics and especially differential geometry, a Kähler manifold is a manifold with three mutually compatible structures: a complex structure, a Riemannian structure, and a symplectic structure.The concept was first studied by Jan Arnoldus Schouten and David van Dantzig in 1930, and then introduced by Erich Kähler in 1933. The terminology has been fixed by André Weil.