Intrinsic metric — In the mathematical study of metric spaces, one can consider the arclength of paths in the space. If two points are a given distance from each other, it is natural to expect that one should be able to get from one point to another along a path… … Wikipedia
Metric expansion of space — Physical cosmology Universe · Big Bang … 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 (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
Glossary of Riemannian and metric geometry — This is a glossary of some terms used in Riemannian geometry and metric geometry mdash; it doesn t cover the terminology of differential topology. The following articles may also be useful. These either contain specialised vocabulary or provide… … 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
Acoustic metric — In mathematical physics, a metric describes the arrangement of relative distances within a surface or volume, usually measured by signals passing through the region – essentially describing the intrinsic geometry of the region. An acoustic metric … Wikipedia
Tensor (intrinsic definition) — For an introduction to the nature and significance of tensors in a broad context, see Tensor. In mathematics, the modern component free approach to the theory of a tensor views a tensor as an abstract object, expressing some definite type of… … Wikipedia
Information geometry — In mathematics and especially in statistical inference, information geometry is the study of probability and information by way of differential geometry. It reached maturity through the work of Shun ichi Amari in the 1980s, with what is currently … Wikipedia
Sub-Riemannian manifold — In mathematics, a sub Riemannian manifold is a certain type of generalization of a Riemannian manifold. Roughly speaking, to measure distances in a sub Riemannian manifold,you are allowed to go only along curves tangent to so called horizontal… … Wikipedia