Related papers: A second-order identity for the Riemann tensor and…
A general expression is given for the quartic Lovelock tensor in terms of the Riemann-Christoffel and Ricci curvature tensors and the Riemann curvature scalar for n-dimensional differentiable manifolds having a general linear connection. In…
We interpret tensors on a smooth manifold M as differential forms over a graded commutative algebra called the algebra of iterated differential forms over M. This allows us to put standard tensor calculus in a new differentially closed…
In linear algebra, the sherman-morrison-woodbury identity says that the inverse of a rank-$k$ correction of some matrix can be computed by doing a rank-k correction to the inverse of the original matrix. This identity is crucial to…
In this paper we introduce, in the Riemannian setting, the notion of conformal Ricci soliton, which includes as particular cases Einstein manifolds, conformal Einstein manifolds and (generic and gradient) Ricci solitons. We provide here…
By using a certain second order differential equation, the notion of adapted coordinates on Finsler manifolds is defined and some classifications of complete Finsler manifolds are found. Some examples of Finsler metrics, with positive…
We consider a class (M, g, q) of four-dimensional Riemannian manifolds M, where besides the metric g there is an additional structure q, whose fourth power is the unit matrix. We use the existence of a local coordinate system such that…
Irreducible bilinear tensorial concomitants of an arbitrary complex antisymmetric valence-2 tensor are derived in four-dimensional spacetime. In addition these bilinear concomitants are symmetric (or antisymmetric), self-dual (or…
We discuss a gap in Besse's book, recently pointed out by Merton, which concerns the classification of Riemannian manifolds admitting a Codazzi tensors with exactly two distinct eigenvalues. For such manifolds, we prove a structure theorem,…
Let $*$ denote the t-product between two third-order tensors. The purpose of this work is to study fundamental computation over the set $St(n,p,l):= \{\mathcal Q\in \mathbb R^{n\times p\times l} \mid \mathcal Q^{\top}* \mathcal Q = \mathcal…
We explicitly establish a unitary correspondence between spherical irreducible tensor operators and cartesian tensor operators of any rank. That unitary relation is implemented by means of a basis of integer-spin wave functions that…
The main object of the present paper is to study the geometric properties of a generalized Roter type semi-Riemannian manifold, which arose in the way of generalization to find the form of the Riemann-Christoffel curvature tensor $R$. Again…
In the literature we see that after introducing a geometric structure by imposing some restrictions on Riemann-Christoffel curvature tensor, the same type structure given by imposing same restriction on other curvature tensors being…
We derive a curvature identity that holds on any 6-dimensional Riemannian manifold, from the Chern-Gauss-Bonnet theorem for a 6-dimensional closed Riemannian manifold. We also introduce some applications of this curvature identity.
Riemann Poisson manifolds were introduced by the author in [1] and studied in more details in [2]. K\"ahler-Riemann foliations form an interesting subset of the Riemannian foliations with remarkable properties (see [3]). In this paper we…
Conformally recurrent pseudo-Riemannian manifolds of dimension n>4 are investigated. The Weyl tensor is represented as a Kulkarni-Nomizu product. If the square of the Weyl tensor is nonzero, a covariantly constant symmetric tensor is…
There are several different notions of "low rank" for tensors, associated to different formats. Among them, the Tensor Train (TT) format is particularly well suited for tensors of high order, as it circumvents the curse of dimensionality:…
We determine the number of functionally independent components of tensors involving higher-order derivatives of a Riemannian metric.
New integral identities satisfied by topological solitons in a range of classical field theories are presented. They are derived by considering independent length rescalings in orthogonal directions, or equivalently, from the conservation…
A general expression is given for the quintic Lovelock tensor as well as for the coefficient of the quintic Lovelock Lagrangian in terms of the Riemann-Christoffel and Ricci curvature tensors and the Riemann curvature scalar for…
The properties of Kaehler submanifolds with recurrent the second fundamental form in spaces of constant holomorphic sectional curvature are being studied in this article.