Ricci Tensor

Some articles on ricci tensor, tensor, ricci:

Sign Convention - Relativity - Curvature
... The Ricci tensor is defined as the contraction of the Riemann tensor ... Due to the symmetries of the Riemann tensor, these two definitions differ by a minus sign ... In fact the second definition of the Ricci tensor is ...
Weyl Tensor - Definition
... The Weyl tensor can be obtained from the full curvature tensor by subtracting out various traces ... This is most easily done by writing the Riemann tensor as a (0,4) valence tensor (by contracting with the metric) ... The (0,4) valence Weyl tensor is then (Petersen 2006, p ...
Schouten Tensor - Further Reading
... Ch.2, noting in a footnote that the Schouten tensor is a "trace-adjusted Ricci tensor" and may be considered as "essentially the Ricci tensor." Wolfgang Kuhnel and Hans-Bert Rademacher, "Conformal diffeomorphisms ...
Ricci Curvature
... In differential geometry, the Ricci curvature tensor, named after Gregorio Ricci-Curbastro, represents the amount by which the volume element of a geodesic ball in a curved Riemannian manifold ... The Ricci tensor is defined on any pseudo-Riemannian manifold, as a trace of the Riemann curvature tensor ... Like the metric itself, the Ricci tensor is a symmetric bilinear form on the tangent space of the manifold (Besse 1987, p ...