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On Classification of Curvature Tensor
American Journal of Physics, 1967A new method for classification of the gravitational field is presented. It is shown that this scheme leads to exactly the same types of gravitational fields as previously obtained by Petrov, Penrose, and Sachs, etc. Some physical applications are also given.
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2011
This chapter studies conformal curvature tensors of a pseudo-Riemannian metric g. These are defined in terms of the covariant derivatives of the curvature tensor of an ambient metric in normal form relative to g. Their transformation laws under conformal change are given in terms of the action of a subgroup of the conformal group O(p + 1, q + 1) on ...
Charles Fefferman, C. Robin Graham
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This chapter studies conformal curvature tensors of a pseudo-Riemannian metric g. These are defined in terms of the covariant derivatives of the curvature tensor of an ambient metric in normal form relative to g. Their transformation laws under conformal change are given in terms of the action of a subgroup of the conformal group O(p + 1, q + 1) on ...
Charles Fefferman, C. Robin Graham
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Iterated tensor voting and curvature improvement
Signal Processing, 2007This research is supported in part by the German–Spanish Academic Research Collaboration Program HA 2001-0087 (DAAD, Acciones integradas Hispano-Alemanas 2002/2003) and the research Grants TEC2004-00834; TEC2005-24739-E; TEC2005-24046-E and PI040765. S.F. and R.R. are supported by a MEC-FPU and a CSIC-I3P fellowship, respectively.
Sylvain Fischer +4 more
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2013
Suppose we have a coordinate system \({x}^{\mu }\) in a region of an \(n\)-dimensional Riemann (or pseudo-Riemann) manifold [20]. Components of the metric tensor \(g_{\mu \nu }\) are given as functions of \({x}^{\mu }\). We want to calculate the Riemann curvature tensor \({R}^{\mu }\,_{\nu \alpha \beta }\) and related quantities (the Ricci tensor \(R_{\
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Suppose we have a coordinate system \({x}^{\mu }\) in a region of an \(n\)-dimensional Riemann (or pseudo-Riemann) manifold [20]. Components of the metric tensor \(g_{\mu \nu }\) are given as functions of \({x}^{\mu }\). We want to calculate the Riemann curvature tensor \({R}^{\mu }\,_{\nu \alpha \beta }\) and related quantities (the Ricci tensor \(R_{\
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Relativity, Tensors, and Curvature
2011Heuristics of Einstein's Theory What does g00 have to do with gravitation? The Metric Potentials Einstein's general theory of relativity is primarily a replacement for Newtonian gravitation and a generalization of special relativity. It cannot be “derived”; we can only speculate, with Einstein, by heuristic reasoning, how such a generalization ...
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Curvature Tensors on Complex Lagrange Spaces
2003Let \((M,L)\) be a complex Lagrange space and let \(T_\mathbb{C} M\) be the complexification of the tangent bundle \(TM\), which is decomposed at each point of \(M\) into \(T_\mathbb{C} M=T'M+T''M\). The author expresses the local coefficients, in the adapted frame of the complex Chern-Lagrange nonlinear connection, of the Levi-Civita connection ...
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On the generalized curvature tensor fields of curvature degree 2.
2000The properties of generalized curvature tensors of degree 2 are studied. A Riemannian manifold \((M,g)\) is considered and, using its Riemannian curvature tensor \(R(X,Y)\) of type \((1,3)\), one defines a generalized curvature tensor of degree \(k\) as a sum of tensor fields each of which contains just \(k\) of Riemannian curvature tensor \(R(X,Y ...
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On the \(C\)-Bochner curvature tensor
TRU Mathematics, 1969MATSUMOTO, MASASTSUNE, CHÛMAN, GORŌ
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