Results 11 to 20 of about 58,187 (222)
Riemann curvature tensor on RCD spaces and possible applications
Comptes Rendus. Mathématique, 2019 We show that, on every RCD space, it is possible to introduce, by a distributional-like approach, a Riemann curvature tensor.Since, after the works of Petrunin and Zhang–Zhu, we know that finite dimensional Alexandrov spaces are RCD spaces, our construction applies in particular to the Alexandrov setting.
N. Gigli
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Normal paracontact metric space form on $W_0$-curvature tensor
Journal of Amasya University the Institute of Sciences and Technology, 2023 In this article, normal paracontact metric space forms are investigated on $W_0$-curvature tensor. Characterizations of normal paracontact space forms are obtained on $W_0$-curvature tensor.
Pakize Uygun +2 more
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Singular Values of Riemann Curvature Tensor [PDF]
, 2018 We introduce the concept of singular values for the Riemann curvature tensor, a central mathematical tool in Einstein's theory of general relativity. We study the properties related to the singular values, and investigate five typical cases to show its relationship to the Ricci scalar and other invariants.
Xiaokai He, Hua Xiang
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The Jordan algebras of Riemann, Weyl and curvature compatible tensors [PDF]
Colloquium Mathematicum, 2021 Given the Riemann, or the Weyl, or a generalized curvature tensor K, a symmetric tensor $b_{ij}$ is named `compatible' with the curvature tensor if $b_i{}^m K_{jklm} + b_j{}^m K_{kilm} + b_k{}^m K_{ijlm} = 0$. Amongst showing known and new properties, we prove that they form a special Jordan algebra, i.e. the symmetrized product of K-compatible tensors
Carlo Alberto Mantica +1 more
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Field Equations for Lovelock Gravity: An Alternative Route
Advances in High Energy Physics, 2018 We present an alternative derivation of the gravitational field equations for Lovelock gravity starting from Newton’s law, which is closer in spirit to the thermodynamic description of gravity. As a warm up exercise, we have explicitly demonstrated that,
Sumanta Chakraborty
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Higher-derivative couplings and torsional Riemann curvature [PDF]
Journal of High Energy Physics, 2022 Using the most general higher-derivative field redefinitions for the closed spacetime manifolds, we show that the tree-level couplings of the metric, B-field and dilaton at orders α′2 and α′3 that have been recently found by the T-duality, can be written
Mohammad R. Garousi
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The Riemann tensor, the metric tensor, and curvature collineations in general relativity [PDF]
Journal of Mathematical Physics, 1982 The equation xμνRμ λαβ+xμλRμ ναβ = 0, where xμν and Rμ ναβ are the components of an arbitrary symmetric tensor and of the Riemann tensor formed from the metric tensor gμν, is trivially satisfied by xμν = φgμν. Nontrivial solutions are important in various areas of general relativity such as in the study of curvature collineations, and also in the study
C. B. G. McIntosh, W. D. Halford
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Incompatible deformation field and Riemann curvature tensor
Applied Mathematics and Mechanics, 2017 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Bohua Sun
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The spectral geometry of the Riemann curvature tensor [PDF]
, 2002 Let E be a natural operator associated to the curvature tensor of a pseudo-Riemannian manifold. This survey article studies when the spectrum, or more generally the real Jordan normal form, of E is constant on the natural domain of definition. It deals with results for the Jacobi operator, the higher order Jacobi operator, the Szabo operator, and the ...
Peter Gilkey, Raina Ivanova, T. Zhang
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Robot grasping and regrasping kinematics using Lie algebra, the geodesic, and Riemann curvature tensor [PDF]
Archives of Control Sciences, 2023 Differential geometry is a strong and highly effective mathematical subject for robot gripper design when grasping within the predetermined trajectories of path planning.
Haydar Sahin
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