Related papers: A New Weyl-like Tensor of Geometric Origin

We make a geometric study of the Geometric Rank of tensors recently introduced by Kopparty et al. Results include classification of tensors with degenerate geometric rank in $C^3\otimes C^3\otimes C^3$, classification of tensors with…

A symmetric tensor is a higher order generalization of a symmetric matrix. In this paper, we study various properties of symmetric tensors in relation to a decomposition into a sum of symmetric outer product of vectors. A rank-1 order-k…

We discuss the algebraic classification of the Weyl tensor in higher dimensional Lorentzian manifolds. This is done by characterizing algebraically special Weyl tensors by means of the existence of aligned null vectors of various orders of…

The algebraic classification of the Weyl tensor in arbitrary dimension n is recovered by means of the principal directions of its "superenergy" tensor. This point of view can be helpful in order to compute the Weyl aligned null directions…

We introduce subspace rank as a tool for studying ranks of tensors and X-rank more generally. We derive a new upper bound for the rank of a tensor and determine the ranks of partially symmetric tensors in C^2 \otimes C^b \otimes C^b. We…

We demonstrate the ``peeling property'' of the Weyl tensor in higher dimensions in the case of even dimensions (and with some additional assumptions), thereby providing a first step towards understanding of the general peeling behaviour of…

The Bel-Robinson tensor is analyzed as a linear map on the space of the traceless symmetric tensors. This study leads to an algebraic classification that refines the usual Petrov-Bel classification of the Weyl tensor. The new classes…

The algebraic study of the Bel-Robinson tensor proposed and initiated in a previous work (Gen. Relativ. Gravit. {\bf 41}, see ref [11]) is achieved. The canonical form of the different algebraic types is obtained in terms of Bel-Robinson…

Higher-order topology yields intriguing multidimensional topological phenomena, while Weyl semimetals have unconventional properties such as chiral anomaly. However, so far, Weyl physics remain disconnected with higher-order topology. Here,…

We construct the tensor hierarchies of generic, bosonic, 5- and 6-dimensional field theories. The construction of the tensor hierarchy starts with the introduction of two tensors: the embedding tensor which tells us which vector is used for…

A tensor is a multi-way array that can represent, in addition to a data set, the expression of a joint law or a multivariate function. As such it contains the description of the interactions between the variables corresponding to each of…

In this paper, we extend some classes of structured matrices to higher order tensors. We discuss their relationships with positive semi-definite tensors and some other structured tensors. We show that every principal sub-tensor of such a…

The well-noted correspondence between gravitation and electrodynamics emphasizes the importance of the Lanczos tensor -- the potential of the Weyl tensor -- which is an inherent structural element of any metric theory of gravity formulated…

We describe a method to generate scalar-tensor theories with Weyl symmetry, starting from arbitrary purely metric higher derivative gravity theories. The method consists in the definition of a conformally-invariant metric $\hat{g}_{\mu…

An attempt is made to uncover the physical meaning and significance of the obscure Lanczos tensor field which is regarded as a potential of the Weyl field. Despite being a fundamental building block of any metric theory of gravity, the…

Vector algebra is a powerful and needful tool for Physics but unfortunately, due to lack of mathematical skills, it becomes misleading for first undergraduate courses of science and engineering studies. Standard vector identities are…

Tensors, or multi-linear forms, are important objects in a variety of areas from analytics, to combinatorics, to computational complexity theory. Notions of tensor rank aim to quantify the "complexity" of these forms, and are thus also…

An extension to higher dimensions of the Bel-Debever characterization of the Weyl tensor is considered. This provides algebraic conditions that uniquely determine the multiplicity of a Weyl aligned null direction (WAND), and thus the…

This educational article highlights the geometric and algebraic complexities that distinguish tensors from matrices, to supplement coverage in advanced courses on linear algebra, matrix analysis, and tensor decompositions. Using the case of…

In all dimensions and arbitrary signature, we demonstrate the existence of a new local potential -- a double (2,3)-form -- for the Weyl curvature tensor, and more generally for all tensors with the symmetry properties of the Weyl curvature…