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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, a lower bound for the dimension p of a vector bundle over a compact Ricci non-negative manifold is established, and it is shown that p admits a complete metric of positive Ricci curvature for all sufficiently large p.
Abstract: If E is the total space of a vector bundle over a compact Ricci non-negative manifold, it is known that E×Rp admits a complete metric of positive Ricci curvature for all sufficiently large p. In this paper we establish a small, explicit lower bound for the dimension p.
10 citations
TL;DR: In this paper, the authors show that the trace of the Chevreton tensor is related to the Bach tensor and use this to find all source-free Einstein-Maxwell spacetimes with a zero cosmological constant that have vanishing Bach tensors.
Abstract: In this paper, we characterize the source-free Einstein–Maxwell spacetimes which have a trace-free Chevreton tensor We show that this is equivalent to the Chevreton tensor being of pure radiation type and that it restricts the spacetimes to Petrov type N or O We prove that the trace of the Chevreton tensor is related to the Bach tensor and use this to find all Einstein–Maxwell spacetimes with a zero cosmological constant that have a vanishing Bach tensor Among these spacetimes we then look for those which are conformal to Einstein spaces We find that the electromagnetic field and the Weyl tensor must be aligned, and in the case that the electromagnetic field is null, the spacetime must be conformally Ricci-flat and all such solutions are known In the non-null case, since the general solution is not known on a closed form, we settle by giving the integrability conditions in the general case, but we do give new explicit examples of Einstein–Maxwell spacetimes that are conformal to Einstein spaces, and we also find examples where the vanishing of the Bach tensor does not imply that the spacetime is conformal to a C-space The non-aligned Einstein–Maxwell spacetimes with vanishing Bach tensor are conformally C-spaces, but none of them are conformal to Einstein spaces
10 citations
TL;DR: From a general Lagrangian that is quadratic in the Ricci tensor, independent variations of the metric and torsion tensors produce gravitational field equations that are of second differential order in the metric tensor as mentioned in this paper.
Abstract: From a general Lagrangian that is quadratic in the Ricci tensor, independent variations of the metric and torsion tensors produce gravitational field equations that are of second differential order in the metric tensor. This reduction in order from four results from the use of the torsional field equations. Also, the equation of motion is derived and several special cases are considered.
10 citations
TL;DR: In this paper, the authors proved properties of the star product of the Weyl type (i.e., associated with Weyl ordering) and the Fedosov construction of the *-product on a two-dimensional phase space with a constant curvature tensor.
10 citations
01 Feb 1984
TL;DR: The main theorem of as discussed by the authors states that every naturally reductive homogeneous Riemannian manifold of nonpositive Ricci curvature is symmetric, and as a corollary, every non-compact symmetric Eigen manifold is also symmetric.
Abstract: The main theorem states that every naturally reductive homogeneous Riemannian manifold of nonpositive Ricci curvature is symmetric. As a corollary, every noncompact naturally reductive Einstein manifold is symmetric.
10 citations