invariant metric

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• Metric (mathematics) — In mathematics, a metric or distance function is a function which defines a distance between elements of a set. A set with a metric is called a metric space. A metric induces a topology on a set but not all topologies can be generated by a metric …   Wikipedia

• Invariant (mathematics) — In mathematics, an invariant is a property of a class of mathematical objects that remains unchanged when transformations of a certain type are applied to the objects. The particular class of objects and type of transformations are usually… …   Wikipedia

• Metric tensor — In the mathematical field of differential geometry, a metric tensor is a type of function defined on a manifold (such as a surface in space) which takes as input a pair of tangent vectors v and w and produces a real number (scalar) g(v,w) in a… …   Wikipedia

• Metric tensor (general relativity) — This article is about metrics in general relativity. For a discussion of metrics in general, see metric tensor. Metric tensor of spacetime in general relativity written as a matrix. In general relativity, the metric tensor (or simply, the metric) …   Wikipedia

• Metric signature — The signature of a metric tensor (or more generally a nondegenerate symmetric bilinear form, thought of as quadratic form) is the number of positive and negative eigenvalues of the metric. That is, the corresponding real symmetric matrix is… …   Wikipedia

• Complete metric space — Cauchy completion redirects here. For the use in category theory, see Karoubi envelope. In mathematical analysis, a metric space M is called complete (or Cauchy) if every Cauchy sequence of points in M has a limit that is also in M or,… …   Wikipedia

• Yamabe invariant — In mathematics, in the field of differential geometry, the Yamabe invariant (also referred to as the sigma constant) is a real number invariant associated to a smooth manifold that is preserved under diffeomorphisms. It was first written down… …   Wikipedia

• Poincaré metric — In mathematics, the Poincaré metric, named after Henri Poincaré, is the metric tensor describing a two dimensional surface of constant negative curvature. It is the natural metric commonly used in a variety of calculations in hyperbolic geometry… …   Wikipedia

• Word metric — In group theory, a word metric on a group G is a way to measure distance between any two elements of G . As the name suggests, the word metric is a metric on G , assigning to any two elements g , h of G a distance d(g,h) that measures how… …   Wikipedia

• Gödel metric — The Gödel metric is an exact solution of the Einstein field equations in which the stress energy tensor contains two terms, the first representing the matter density of a homogeneous distribution of swirling dust particles, and the second… …   Wikipedia

• Seiberg–Witten invariant — In mathematics, Seiberg–Witten invariants are invariants of compact smooth 4 manifolds introduced by harvtxt|Witten|1994, using the Seiberg Witten theory studied by harvs|txt=yes|last=Seiberg|last2=Witten|year1=1994a|year2=1994b during their… …   Wikipedia