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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: For every nonholonomic manifold, i.e., manifold with nonintegrable distribution the analog of the Riemann tensor is introduced in this paper, which is interpreted as modiÞcations of the Spencer cohomology.
Abstract: For every nonholonomic manifold, i.e., manifold with nonintegrable distribution the analog of the Riemann tensor is introduced. It is calculated here for the contact and Engel structures: for the contact structure it vanishes (another proof of Darboux’s canonical form); for the Engel distribution the target space of the tensor is of dimension 2. In particular, the Lie algebra preserving the Engel distribution is described. The tensors introduced are interpreted as modiÞcations of the Spencer cohomology and, as such, provide with a new way
23 citations
TL;DR: In this article, the authors classify all non-Kahler almost Kahler 4-manifolds for which the fundamental 2-form is an eigenform of the Weyl tensor, and whose Ricci tensor is invariant with respect to the almost complex structure.
Abstract: We classify, up to a local isometry, all non-Kahler almost Kahler 4-manifolds for which the fundamental 2-form is an eigenform of the Weyl tensor, and whose Ricci tensor is invariant with respect to the almost complex structure. Equivalently, such almost Kahler 4-manifolds satisfy the third curvature condition of A. Gray. We use our local classification to show that, in the compact case, the third curvature condition of Gray is equivalent to the integrability of the corresponding almost complex structure.
23 citations
23 citations
TL;DR: In this article, the reconstruction problem of a compactly supported symmetric tensor field in ℝn, if its ray transform is known along the lines, intersecting a given curve, is studied.
Abstract: Abstract - The paper is devoted to the reconstruction problems of a compactly supported symmetric tensor field in ℝn , if its ray transform is known along the lines, intersecting a given curve. Two versions of the reconstruction are considered.
23 citations
TL;DR: In this paper, the algebraic consequences for the Weyl and Ricci tensors are examined in detail and consideration given to the uniqueness of ua is made concerning the nature of the congruence associated with ua.
Abstract: Purely magnetic space–times, in which the Riemann tensor satisfies Rabcdubud=0 for some unit timelike vector ua, are studied. The algebraic consequences for the Weyl and Ricci tensors are examined in detail and consideration given to the uniqueness of ua. Some remarks concerning the nature of the congruence associated with ua are made.
23 citations