Keywords

#intrinsic_metric

Intrinsic metric

Concept in geometry/topology

In the mathematical study of metric spaces, one can consider the arclength of paths in the space. If two points are at a given distance from each other, it is natural to expect that one should be able to get from the first point to the second along a path whose arclength is equal to that distance. The distance between two points of a metric space relative to the intrinsic metric is defined as the infimum of the lengths of all paths from the first point to the second. A metric space is a length metric space if the intrinsic metric agrees with the original metric of the space.

Sat 18th

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Intrinsic metric Riemannian manifold Sub-Riemannian manifold Metric space Expansion of the universe Glossary of Riemannian and metric geometry Geodesic Finsler manifold Metric tensor Metric tensor (general relativity)
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