Related papers: Unique characterization of the Bel-Robinson tensor

Let V be a rank N vector bundle on a d-dimensional complex projective scheme X; assume that V is equipped with a skew-symmetric bilinear form with values in a line bundle L and that \Lambda^2 V^* \otimes L is ample. Suppose that the maximum…

The tensor rank decomposition, or canonical polyadic decomposition, is the decomposition of a tensor into a sum of rank-1 tensors. The condition number of the tensor rank decomposition measures the sensitivity of the rank-1 summands with…

In this work, we present a new characterization of symmetric $H^+$-tensors. It is known that a symmetric tensor is an $H^+$-tensor if and only if it is a generalized diagonally dominant tensor with nonnegative diagonal elements. By…

The Robinson-Trautman solution in the Einstein-Maxwell-$\Lambda$ system admits a shear-free and twist-free null geodesic congruence with a nonvanishing expansion. Restricting to the case where the Maxwell field is aligned, i.e., the…

A special class of (complex) para-Hermite Einstein spaces is analyzed. For this class of spaces the self-dual Weyl tensor is type-[D] in the Petrov-Penrose classification. The anti-self-dual Weyl tensor is algebraically degenerate,…

A renormalizable rigid supersymmetry for the four dimensional antisymmetric tensor field model in a curved space-time background is constructed. A closed algebra between the BRS and the supersymmetry operators is only realizable if the…

We consider the problem of low canonical polyadic (CP) rank tensor completion. A completion is a tensor whose entries agree with the observed entries and its rank matches the given CP rank. We analyze the manifold structure corresponding to…

We derive, using the pure-spinor formalism, the complete -- including the fermions -- four-point effective action of both type II superstrings to all orders in $\alpha'$, at tree level in string loops. We find that, in the quartic-field…

Asymptotic tensor rank is notoriously difficult to determine. Indeed, determining its value for the $2\times 2$ matrix multiplication tensor would determine the matrix multiplication exponent, a long-standing open problem. On the other…

A concise geometrical formulation of N=4 supergravity containing an antisymmetric tensor gauge field is given in central charge superspace: graviphotons are identified in the super-vielbein on the same footing as the vierbein and the…

Stimulated by odd-bipartite and even-bipartite hypergraphs, we define odd-bipartite (weakly odd-bipartie) and even-bipartite (weakly even-bipartite) tensors. It is verified that all even order odd-bipartite tensors are irreducible tensors,…

We first prove two new spectral properties for symmetric nonnegative tensors. We prove a maximum property for the largest H-eigenvalue of a symmetric nonnegative tensor, and establish some bounds for this eigenvalue via row sums of that…

A theorem of J. Kruskal from 1977, motivated by a latent-class statistical model, established that under certain explicit conditions the expression of a 3-dimensional tensor as the sum of rank-1 tensors is essentially unique. We give a new…

It is shown that in every dimension n=3j+2, j=1,2,3,..., there exist compact pseudo-Riemannian manifolds with parallel Weyl tensor, which are Ricci-recurrent, but neither conformally flat nor locally symmetric, and represent all indefinite…

We investigate the geometry of a twisting non-shearing congruence of null geodesics on a conformal manifold of even dimension greater than four and Lorentzian signature. We give a necessary and sufficient condition on the Weyl tensor for…

Given tensors $T$ and $T'$ of order $k$ and $k'$ respectively, the tensor product $T \otimes T'$ is a tensor of order $k+k'$. It was recently shown that the tensor rank can be strictly submultiplicative under this operation…

A tensor $T$, in a given tensor space, is said to be $h$-identifiable if it admits a unique decomposition as a sum of $h$ rank one tensors. A criterion for $h$-identifiability is called effective if it is satisfied in a dense, open subset…

This paper studies symmetric tensor decompositions. For symmetric tensors, there exist linear relations of recursive patterns among their entries. Such a relation can be represented by a polynomial, which is called a generating polynomial.…

Let A be a unital separable simple C*-algebra with a unique tracial state. We prove that if A is nuclear and quasidiagonal, then A tensored with the universal UHF-algebra has decomposition rank at most one. Then it is proved that A is…

Inspired by recent work of Kopparty-Moshkovitz-Zuiddam and motivated by problems in combinatorics and hypergraphs, we introduce the notion of the symmetric geometric rank of a symmetric tensor. This quantity is equal to the codimension of…