Related papers: A General Expression for the Quintic Lovelock Tens…

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…

This paper presents some possible features of general expressions for Lovelock tensors and for the coefficients of Lovelock Lagrangians up to the 15th order in curvature (and beyond) in terms of the Riemann-Christoffel and Ricci curvature…

Some general expressions are given for the coefficient of the 14th Chern form in terms of the Riemann-Christoffel curvature tensor and some of its concomitants (e.g., Pontrjagin's characteristic tensors) for n-dimensional differentiable…

General expressions are given for the coefficients of Chern forms up to the 13th order in curvature in terms of the Riemann-Christoffel curvature tensor and some of its concomitants (e.g., Pontrjagin's characteristic tensors) for…

We show that the splitting feature of the Einstein tensor, as the first term of the Lovelock tensor, into two parts, namely the Ricci tensor and the term proportional to the curvature scalar, with the trace relation between them is a common…

For any semi-Riemannian manifold (M,g) we define some generalized curvature tensor as a linear combination of Kulkarni-Nomizu products formed by the metric tensor, the Ricci tensor and its square of given manifold. That tensor is closely…

Let $(M,g)$ be a Riemannian manifold, and $m$ be a second metric on $M$. We give expressions of $m$'s associated connection, and Riemann curvature tensor $R_m$, in terms of $R_g$ and certain combinations of covariant derivatives of $m$…

In the Riemann geometry, the metric's equation of motion for an arbitrary Lagrangian is succinctly expressed in term of the first variation of the action with respect to the Riemann tensor if the Riemann tensor were independent of the…

We define the notion of the Ricci tensor for NQ symplectic manifolds of degree 2 and show that it corresponds to the standard generalized Ricci tensor on Courant algebroids. We use an appropriate notion of connections compatible with the…

In this paper, we propose a generalization of the Riemann curvature tensor on manifolds (of dimension two or higher) endowed with a Regge metric. Specifically, while all components of the metric tensor are assumed to be smooth within…

A second-order differential identity for the Riemann tensor is obtained, on a manifold with symmetric connection. Several old and some new differential identities for the Riemann and Ricci tensors descend from it. Applications to manifolds…

It is possible to define an analogue of the Riemann tensor for $N$th order Lovelock gravity, its characterizing property being that the trace of its Bianchi derivative yields the corresponding analogue of the Einstein tensor. Interestingly…

It is generalized Weyl conformal curvature tensor in the case of a conformal mappings of a generalized Riemannian space in this paper. Moreover, it is found universal generalizations of it without any additional assumption. A method used in…

We present a tensor calculus for exceptional generalised geometry. Expressions for connections, torsion and curvature are given a unified formulation for different exceptional groups E_n(n). We then consider "tensor gauge fields" coupled to…

The classification of all fourth-order anisotropic tensor classes for classical linear elasticity is well known. In this article, we review the related problem of explicitly computing the dimension and the expressions of the elements…

Lovelock terms are polynomial scalar densities in the Riemann curvature tensor that have the remarkable property that their Euler-Lagrange derivatives contain derivatives of the metric of order not higher than two (while generic polynomial…

For spherical symmetry, we provide expressions for the radial null-null components of the generalized Einstein tensor $E_{ab}$ for Lovelock models for diagonal $E_{ab}$ in terms of the metric and of the radial null-null components of the…

A generalized Clifford manifold is proposed in which there are coordinates not only for the basis vector generators, but for each element of the Clifford group, including the identity scalar. These new quantities are physically interpreted…

Derdzinski and Shen's theorem on the restrictions posed by a Codazzi tensor on the Riemann tensor holds more generally when a Riemann-compatible tensor exists. Several properties are shown to remain valid in this broader setting. Riemann…

A general expression is given for the 14th Chern form in terms of simple polynomial concomitants of the curvature 2-form for n-dimensional differentiable manifolds having a general linear connection.