usual metric
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metric space — Math. a space with a metric defined on it. [1925 30] * * * In mathematics, a set of objects equipped with a concept of distance. The objects can be thought of as points in space, with the distance between points given by a distance formula, such… … Universalium
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 derivative — In mathematics, the metric derivative is a notion of derivative appropriate to parametrized paths in metric spaces. It generalizes the notion of speed or absolute velocity to spaces which have a notion of distance (i.e. metric spaces) but not… … 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
Convex metric space — An illustration of a convex metric space. In mathematics, convex metric spaces are, intuitively, metric spaces with the property any segment joining two points in that space has other points in it besides the endpoints. Formally, consider a… … Wikipedia
Kerr-Newman metric — The Kerr Newman metric is a solution of Einstein s general relativity field equation that describes the spacetime geometry in the region surrounding a charged, rotating mass. Like the Kerr metric, the interior solution exists mathematically and… … Wikipedia
Wasserstein metric — In mathematics, the Wasserstein (or Vasershtein) metric is a distance function defined between probability distributions on a given metric space M. Intuitively, if each distribution is viewed as a unit amount of dirt piled on M, the metric is the … Wikipedia
Fubini-Study metric — In mathematics, the Fubini Study metric is a Kähler metric on projective Hilbert space, that is, complex projective space CP n endowed with a Hermitian form. In the context of quantum mechanics, for n=1 this space is called the Bloch sphere; the… … Wikipedia
Reissner-Nordström metric — In physics and astronomy, the Reissner Nordström metric is a solution to the Einstein field equations in empty space, which corresponds to the gravitational field of a charged, non rotating, spherically symmetric body of mass M . Discovered by… … Wikipedia
Uniform space — In the mathematical field of topology, a uniform space is a set with a uniform structure. Uniform spaces are topological spaces with additional structure which is used to define uniform properties such as completeness, uniform continuity and… … Wikipedia
Ricci flow — In differential geometry, the Ricci flow is an intrinsic geometric flow a process which deforms the metric of a Riemannian manifold in this case in a manner formally analogous to the diffusion of heat, thereby smoothing out irregularities in the… … Wikipedia
