Difference between revisions of "Curvature is antisymmetric in last two variables"
(Created page with '==Statement== Suppose <math>M</math> is a differential manifold and <math>g</math> is a fact about::Riemannian metric or fact about::pseudo-Riemannian metric and <ma…')
Revision as of 01:28, 24 July 2009
Suppose is a differential manifold and is a Riemannian metric or pseudo-Riemannian metric and is the Levi-Civita connection for . Consider the Riemann curvature tensor of . In other words, is the Riemann curvature tensor of the Levi-Civita connection for . We can treat as a -tensor:
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