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Sub-Lorentzian Geometry of Curves and Surfaces in a Lorentzian Lie Group
Advances in Mathematical Physics, 2022 We consider the sub-Lorentzian geometry of curves and surfaces in the Lie group E1,1. Firstly, as an application of Riemannian approximants scheme, we give the definition of Lorentzian approximants scheme for E1,1 which is a sequence of Lorentzian ...
Haiming Liu, Jianyun Guan
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Relativistic cosmology and intrinsic spin of matter: Results and theorems in Einstein-Cartan theory [PDF]
Physical Review D 107, 084004 (2023), 2023 We start by presenting the general set of structure equations for the 1+3 threading spacetime decomposition in 4 spacetime dimensions, valid for any theory of gravitation based on a metric compatible affine connection. We then apply these equations to the study of cosmological solutions of the Einstein-Cartan theory in which the matter is modeled by a ...
arxiv +1 more source
Intrinsic spin Nernst effect of magnons in a noncollinear antiferromagnet
Physical Review Research, 2020 We investigate the intrinsic magnon spin current in a noncollinear antiferromagnetic insulator. We introduce a definition of the magnon spin current in a noncollinear antiferromagnet and find that it is in general nonconserved, but for certain symmetries
Bo Li +2 more
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Journal of the American Statistical Association, 2009 The aim of this paper is to develop an intrinsic regression model for the analysis of positive-definite matrices as responses in a Riemannian manifold and their association with a set of covariates, such as age and gender, in a Euclidean space. The primary motivation and application of the proposed methodology is in medical imaging.
Zhu, Hongtu +5 more
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On the measurement predictions concerning the intrinsic relativistic spin operator [PDF]
arXiv, 2021 Although there are several proposals of relativistic spin in the literature, the recognition of intrinsicality as a key characteristic for the definition of this concept is responsible for selecting a single tensor operator that adequately describes such a quantity.
arxiv
The Berry Phase Rectification Tensor and The Solar Rectification Vector [PDF]
Journal of Physics D: Applied Physics 2021, 2020 We introduce an operational definition of the Berry Phase Rectification Tensor as the second-order change of polarization of a material in response to an ideal short pulse of an electric field. Under time-reversal symmetry this tensor depends exclusively on the Berry phases of the Bloch bands and not their energy dispersions, making it an intrinsic ...
arxiv +1 more source
Tensor Generalizations of Affine Symmetry Vectors [PDF]
J.Math.Phys.50:122506,2009, 2009 A definition is suggested for affine symmetry tensors, which generalize the notion of affine vectors in the same way that (conformal) Killing tensors generalize (conformal) Killing vectors. An identity for these tensors is proved, which gives the second derivative of the tensor in terms of the curvature tensor, generalizing a well-known identity for ...
arxiv +1 more source
Basis-Free Analysis of Singular Tuples and Eigenpairs of Tensors [PDF]
arXiv, 2020 A tensor in applied mathematics is usually defined as a multidimensional array of numbers. This presumes a choice of basis in $\mathbb{R}^n$ or in some other vector space, and tensorial concepts are defined accordingly. In this article we define eigenvalues, eigenvectors, singular values, and singular vectors of a tensor intrinsically, without ...
arxiv
The tensor t-function: a definition for functions of third-order tensors [PDF]
, 2018 A definition for functions of multidimensional arrays is presented. The definition is valid for third-order tensors in the tensor t-product formalism, which regards third-order tensors as block circulant matrices. The tensor function definition is shown to have similar properties as standard matrix function definitions in fundamental scenarios.
arxiv +1 more source
Null Geodesic Congruences, Asymptotically-Flat Spacetimes and Their Physical Interpretation
Living Reviews in Relativity, 2009 A priori, there is nothing very special about shear-free or asymptotically shear-free null geodesic congruences. Surprisingly, however, they turn out to possess a large number of fascinating geometric properties and to be closely related, in the context ...
Timothy M. Adamo +2 more
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