Cotangent space & Minkowski space - Unionpedia, the concept map

Shortcuts: Differences, Similarities, Jaccard Similarity Coefficient, References.

Difference between Cotangent space and Minkowski space

Cotangent space vs. Minkowski space

In differential geometry, the cotangent space is a vector space associated with a point x on a smooth (or differentiable) manifold \mathcal M; one can define a cotangent space for every point on a smooth manifold. In physics, Minkowski space (or Minkowski spacetime) is the main mathematical description of spacetime in the absence of gravitation.

Differential form

In mathematics, differential forms provide a unified approach to define integrands over curves, surfaces, solids, and higher-dimensional manifolds.

Cotangent space and Differential form · Differential form and Minkowski space · See more »

Differential geometry

Differential geometry is a mathematical discipline that studies the geometry of smooth shapes and smooth spaces, otherwise known as smooth manifolds.

Cotangent space and Differential geometry · Differential geometry and Minkowski space · See more »

Dual space

In mathematics, any vector space V has a corresponding dual vector space (or just dual space for short) consisting of all linear forms on V, together with the vector space structure of pointwise addition and scalar multiplication by constants.

Cotangent space and Dual space · Dual space and Minkowski space · See more »

Linear form

In mathematics, a linear form (also known as a linear functional, a one-form, or a covector) is a linear mapIn some texts the roles are reversed and vectors are defined as linear maps from covectors to scalars from a vector space to its field of scalars (often, the real numbers or the complex numbers).

Cotangent space and Linear form · Linear form and Minkowski space · See more »

One-form (differential geometry)

In differential geometry, a one-form (or covector field) on a differentiable manifold is a differential form of degree one, that is, a smooth section of the cotangent bundle.

Cotangent space and One-form (differential geometry) · Minkowski space and One-form (differential geometry) · See more »

Pullback (differential geometry)

Let \phi:M\to N be a smooth map between smooth manifolds M and N. Then there is an associated linear map from the space of 1-forms on N (the linear space of sections of the cotangent bundle) to the space of 1-forms on M. This linear map is known as the pullback (by \phi), and is frequently denoted by \phi^*.

Cotangent space and Pullback (differential geometry) · Minkowski space and Pullback (differential geometry) · See more »

Pushforward (differential)

In differential geometry, pushforward is a linear approximation of smooth maps (formulating manifold) on tangent spaces.

Cotangent space and Pushforward (differential) · Minkowski space and Pushforward (differential) · See more »

Real number

In mathematics, a real number is a number that can be used to measure a continuous one-dimensional quantity such as a distance, duration or temperature.

Cotangent space and Real number · Minkowski space and Real number · See more »

Riemannian manifold

In differential geometry, a Riemannian manifold is a geometric space on which many geometric notions such as distance, angles, length, volume, and curvature are defined.

Cotangent space and Riemannian manifold · Minkowski space and Riemannian manifold · See more »

Springer Science+Business Media

Springer Science+Business Media, commonly known as Springer, is a German multinational publishing company of books, e-books and peer-reviewed journals in science, humanities, technical and medical (STM) publishing.

Cotangent space and Springer Science+Business Media · Minkowski space and Springer Science+Business Media · See more »

Tangent space

In mathematics, the tangent space of a manifold is a generalization of to curves in two-dimensional space and to surfaces in three-dimensional space in higher dimensions.

Cotangent space and Tangent space · Minkowski space and Tangent space · See more »

Vector space

In mathematics and physics, a vector space (also called a linear space) is a set whose elements, often called ''vectors'', can be added together and multiplied ("scaled") by numbers called ''scalars''.

Cotangent space and Vector space · Minkowski space and Vector space · See more »