Fundamental theorem of Riemannian geometry
Unique existence of the Levi-Civita connection / From Wikipedia, the free encyclopedia
Dear Wikiwand AI, let's keep it short by simply answering these key questions:
Can you list the top facts and stats about Fundamental theorem of Riemannian geometry?
Summarize this article for a 10 year old
SHOW ALL QUESTIONS
In the mathematical field of Riemannian geometry, the fundamental theorem of Riemannian geometry states that on any Riemannian manifold (or pseudo-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.