2009 | OriginalPaper | Buchkapitel
Ricci curvature
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Curvature is a generic name to designate a local invariant of a metric space that quantifies the deviation of this space from being Euclidean. (Here “local invariant” means a quantity which is invariant under local isometries.) It is standard to define and study curvature mainly on Riemannian manifolds, for in that setting definitions are rather simple, and the Riemannian structure allows for “explicit” computations. Throughout this chapter,
M
will stand for a complete connected Riemannian manifold, equipped with its metric
g
.