Fundamental theorem of Riemannian geometry
id:
fundamental-theorem-of-riemannian-geometry-196-18607938
title:
Fundamental theorem of Riemannian geometry
text:
In the mathematical field of Riemannian geometry, the fundamental theorem of Riemannian geometry states that on any Riemannian manifold there is a unique affine connection that is torsion-free and metric-compatible, called the Levi-Civita connection or (pseudo-)Riemannian connection of the given metric. Because it is canonically defined by such properties, often this connection is automatically used when given a metric.
brand slug:
wiki
category slug:
encyclopedia
description:
Unique existence of the Levi-Civita connection
original url:
https://en.wikipedia.org/wiki/Fundamental_theorem_of_Riemannian_geometry
date created:
date modified:
2022-11-05T17:26:32Z
main entity:
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image:
fields total:
13
integrity:
14