Difference between revisions of "Curvaturetransitive metric"
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Latest revision as of 19:36, 18 May 2008
This article defines a property that makes sense for a Riemannian metric over a differential manifold
Contents
Definition
Symbolfree definition
A Riemannian metric on a differential manifold] is termed curvaturetransitive if given any two points with the same sectional curvature, there is an isometry of the manifold taking one to the other.
In other words, the sectional curvature is a complete invariant of the isometry class of a point.