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HYPERSURFACES WITH PARALLEL RICCI TENSOR
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Collineations of the Ricci tensor
Journal of Mathematical Physics, 1993Ricci collineations for the Ricci tensor which is constructed from a general spherically symmetric and static metric are classified for all possibilities of Rab(r) (such that Rab≠0 for a=b). It turns out that the only collineations admitted by this tensor can be ten, six, or four and there does not appear any case in between.
Ashfaque Bokhari +2 more
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On the Curvature of Kähler Manifolds with Zero Ricci Tensor
Mathematical Notes, 2019zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Riemann curvature and the Ricci tensor
Abstract In Chapter 11, we explain how curvature of spaces are described using the Riemann tensor and the Ricci tensor. These will supply the left-hand side of the Einstein equation. Geodesic deviation allows us to identify tidal forces that result from the curvature of spacetime due to gravity.Tom Lancaster, Stephen J. Blundell
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Modifications of the Ricci tensor and applications
Archiv der Mathematik, 2010By using two modified Ricci tensors, we prove some theorems which correspond to Myers’s diameter estimate theorem and Bochner’s vanishing theorem.
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The Ricci tensor of a diagonal metric
American Journal of Physics, 1995Formulas in suffix notation are obtained for the general diagonal component and the general off-diagonal component of the Ricci tensor of a pseudo-Riemannian manifold of arbitrary dimension with diagonal metric. Two applications to general relativity are briefly considered.
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Ricci tensor with six collineations
International Journal of Theoretical Physics, 1992zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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A theorem of Ambrose for Bakry–Emery Ricci tensor
Annals of Global Analysis and Geometry, 2013zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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