metric geometry

The essential difference between the metric geometries is the nature of parallel lines.

In the language of metric geometry, it is invariant under quasi-isometries.

In metric geometry an automorphism is a self-isometry.

But probed at a macroscopic scale, it appears as a three-dimensional continuous metric geometry.

Geodesics are commonly seen in the study of Riemannian geometry and more generally metric geometry.

In metric geometry, a geodesic is a curve which is everywhere locally a distance minimizer.

Glossary of Riemannian and metric geometry.

In mathematics, specifically in metric geometry, a polyhedral space is a certain metric space.

Other important areas include metric geometry of polyhedra, such as the Cauchy theorem on rigidity of convex polytopes.

Though Euclidean geometry is both affine and metric geometry, in general affine spaces may be missing a metric.

This is a glossary of some terms used in Riemannian geometry and metric geometry - it doesn't cover the terminology of differential topology.

More generally, the term motion is a synonym for surjective isometry in metric geometry, including elliptic geometry and hyperbolic geometry.

More generally, the Ricci tensor can be defined in broader class of metric geometries (by means of the direct geometric interpretation, below) that includes Finsler geometry.

In metric geometry, the metric envelope or tight span of a metric space M is an injective metric space into which M can be embedded.

In metric geometry, the Cartan-Hadamard theorem is the statement that the universal cover of a connected non-positively curved complete metric space X is a Hadamard space.

A caveat: many terms in Riemannian and metric geometry, such as convex function, convex set and others, do not have exactly the same meaning as in general mathematical usage.

Because of this city layout, in metric geometry, Karlsruhe metric refers to a measure of distance that assumes travel is only possible along radial streets and along circular avenues around the centre.

In this approach, the metric geometry of probability distributions is studied; this approach quantifies approximation error with, for example, the Kullback-Leibler distance, Bregman divergence, and the Hellinger distance.

For that goal a group at the Technion applied tools from metric geometry to treat expressions as isometries A company called Vision Access created a firm solution for 3D facial recognition.

Lemaître developed the theory of quaternions from first principles so that his essay can stand on its own, but he recalled the Erlangen program in geometry while developing the metric geometry of elliptic space.

To explain the backward attitude to Clifford, they point out that he was an expert in metric geometry, and "metric geometry was too challenging to orthodox epistemology to be pursued."

As Euclidean geometry lies at the intersection of metric geometry and affine geometry, non-Euclidean geometry arises when either the metric requirement is relaxed, or the parallel postulate is set aside.

It includes Functional Equations, Approximation Theory, Global Analysis, Analysis on Manifolds, Calculus of Variations, Nonlinear Functional Analysis, Inequalities, Metric Geometry and their Applications.

In metric geometry, an injective metric space, or equivalently a hyperconvex metric space, is a metric space with certain properties generalizing those of the real line and of L distances in higher-dimensional vector spaces.

Mathematically, the theory is modelled after Bernhard Riemann's metric geometry, but the Lorentz group of spacetime symmetries (an essential ingredient of Einstein's own theory of special relativity) replaces the group of rotational symmetries of space.