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Ricci decomposition
About: Ricci decomposition is a research topic. Over the lifetime, 1972 publications have been published within this topic receiving 45295 citations.
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TL;DR: In this paper, the authors studied Weyl-pseudosymmetric generalized Sasakianspace-forms and such space-forms satisfying the conditions C(ξ,X)R = 0 and C(X,S)S = 0, where R and S are the Riemannian curvature tensors and the Ricci tensor, respectively.
Abstract: The object of the this paper is to study Weyl-pseudosymmetric generalized Sasakianspace-forms and such space-forms satisfying the conditions C(ξ,X)R = 0 and C(ξ,X)S = 0, where C is the Weyl-conformal curvature tensor, R and S are the Riemannian curvature tensor and the Ricci tensor of the space-form respectively.
15 citations
TL;DR: The necessary and sufficient conditions for a three-dimensional Lorentzian metric to admit a group of isometries acting on s-dimensional orbits are given in this article in terms of the eigenvalues and eigenvectors of the Ricci tensor.
Abstract: The necessary and sufficient conditions for a three‐dimensional Lorentzian metric to admit a group Gr of isometries acting on s‐dimensional orbits are given. These conditions are expressed in terms of the eigenvalues and eigenvectors of the Ricci tensor. As a by‐product, the set of (abstract) groups that can act isometrically and maximally on such metrics is obtained.
15 citations
TL;DR: In this article, the authors introduced a new notion of pseudo-anti commuting Ricci tensor for real hypersurfaces in the complex quadric Q m = S O m + 2 /S O 2 s O m.
15 citations
TL;DR: In this article, the authors discuss Levi-Civita connections on Courant algebroids and compute the corresponding scalar curvatures in the exact and heterotic case, leading to generalized (bosonic) Einstein-Hilbert type of actions known from supergravity.
15 citations
TL;DR: In this article, the role of the Weyl curvature tensor in static sources of the Schwarzschild field is studied, and it is shown that the contribution from the tensor to the mass-energy inside the body may be positive, negative, or zero.
Abstract: The role of the Weyl curvature tensor in static sources of the Schwarzschild field is studied. It is shown that in general the contribution from the Weyl curvature tensor (the ``purely gravitational field energy'') to the mass-energy inside the body may be positive, negative, or zero. It is proved that a positive (negative) contribution from the Weyl tensor tends to increase (decrease) the effective gravitational mass, the red-shift (from a point in the sphere to infinity), as well as the gravitational force which acts on a constituent matter element of a body. It is also proved that the contribution from the Weyl tensor always is negative in sources with surface gravitational potential larger than (4/9. It is pointed out that large negative contributions from the Weyl tensor could give rise to the phenomenon of gravitational repulsion. A simple example which illustrates the results is discussed.
15 citations