In mathematics , especially differential geometry , the
cotangent bundle of a smooth manifold is the vector bundle of all the
cotangentKaynak: Cotangent bundleIn differential geometry , one can attach to every point x of a smooth (or differentiable) manifold a vector space called the
cotangentKaynak: Cotangent spaceIn mathematics the
cotangent complex is a roughly a universal linearization of a morphism of geometric or algebraic objects.
Kaynak: Cotangent complexIn mathematics, Hermite's
cotangent identity is a trigonometric identity discovered by Charles Hermite Suppose a 1, ..., a n are
Kaynak: Hermite's cotangent identityIn mathematics, a Størmer number or arc-
cotangent irreducible number, named after Carl Størmer , is a positive integer n for which the
Kaynak: Størmer numberhyperbolic functions are periodic with respect to the imaginary component, with period 2 pi i (pi i for hyperbolic tangent and
cotangent). | +
Kaynak: Hyperbolic functionFundamental examples are the holomorphic tangent bundle of a complex manifold, and its dual, the holomorphic
cotangent bundle.
Kaynak: Holomorphic vector bundleThe
cotangent space of a local ring R, with maximal ideal m is defined to be: mathfrak m/mathfrak m^2 where m 2 is given by the product
Kaynak: Zariski tangent spaceA section of TM is a vector field on M, and the dual bundle to TM is the
cotangent bundle , which is the disjoint union of the
Kaynak: Tangent bundleIn mathematics , the tautological one-form is a special 1-form defined on the
cotangent bundle T Q of a manifold Q. The exterior
Kaynak: Tautological one-formsections of the
cotangent bundle ) to the space of 1-forms on M. This linear map is known as the pullback (by φ), and is frequently denoted by φ.
Kaynak: Pullback (differential geometry)the
cotangent space of configuration space ). The concept of phase space was developed in the late 19th century by Ludwig Boltzmann ,
Kaynak: Phase spaceIn mathematics , a quadratic differential on a Riemann surface is a section of the symmetric square of the holomorphic
cotangent bundle .
Kaynak: Quadratic differentialin classical mechanics may be generalized to a more abstract 20th century definition of coordinates on the
cotangent bundle of a manifold
Kaynak: Canonical coordinates