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Ricci tensor

   Also found in: Wikipedia 0.01 sec.
Ricci tensor [′rē‚chē ‚ten·sər]


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A Riemannian manifold M is said to be semi-Einstein if Ricci tensor S, which is non-zero, satisfies S(X,Y) = P(Z)g(X,Y) [for all]X,Y,Z[member of]TM (4) and P is a non-zero 1-form, such that the vector fields are not scalar multiple of a single vector.
PRELIMINARIES An n-dimensional Riemannian manifold (M,g), n > 2, is said to be an Einstein manifold if its Ricci tensor S satisfies the condition S = r/n g, where r denotes the scalar curvature of M.
135 QA670 This is the first volume of a two-part sequel of The Ricci Flow: An Introduction by the same authors, which laid out the foundations for the study of Richard Hamilton's Ricci flow, an evolution equation which deforms Riemannian metrics by evolving them in the direction of minus the Ricci tensor.
 
 
 
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