definite metric
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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
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
Karp-Flatt metric — The Karp Flatt Metric is a measure of parallelization of code in parallel processor systems. This metric exists in addition to Amdahl s Law and the Gustafson s Law as an indication of the extent to which a particular computer code is parallelized … Wikipedia
Bergman metric — In differential geometry, the Bergman metric is a Hermitian metric that can be defined on certain types of complex manifold. It is so called because it is derived from the Bergman kernel.DefinitionLet G subset {mathbb{C^n be a domain and let… … Wikipedia
Riemannian manifold — In Riemannian geometry, a Riemannian manifold ( M , g ) (with Riemannian metric g ) is a real differentiable manifold M in which each tangent space is equipped with an inner product g in a manner which varies smoothly from point to point. The… … Wikipedia
Metrication in the United Kingdom — The metric and imperial systems of measurement are used side by side in the United Kingdom: Eurostar s design speed is cited both as 300 km/h [1] and as 186 mph .[2] Metrication in the United Kingdom is the pr … Wikipedia
Alcubierre drive — The Alcubierre metric, also known as the Alcubierre drive or Warp Drive, is a speculative mathematical model of a spacetime exhibiting features reminiscent of the fictional warp drive from Star Trek , which can travel Faster than light (although… … Wikipedia
Signature change — is concerned with when the signature of spacetime can change from positive definite (++++) to Lorentzian ( +++).There are several reasons for interest in signature change including:1) In the early universe there might be a transition from… … Wikipedia
Generalized complex structure — In the field of mathematics known as differential geometry, a generalized complex structure is a property of a differential manifold that includes as special cases a complex structure and a symplectic structure. Generalized complex structures… … Wikipedia
Cartan-Karlhede algorithm — One of the most fundamental problems of Riemannian geometry is this: given two Riemannian manifolds of the same dimension, how can one tell if they are locally isometric? This question was addressed by Elwin Christoffel, and completely solved by… … Wikipedia
