Remarks on the algebraic structure of (2, 2) double forms
General Relativity and Quantum Cosmology
2024-12-24 v1 Mathematical Physics
Differential Geometry
math.MP
Abstract
We study the algebraic features of covariant tensors of valence four containing two blocks of skew indices. After a rather general treatment, we specialize ourselves to four-dimensional spacetimes and discuss several complementary aspects of these objects. In particular, we focus our attention on the corresponding invariant subspaces and generalise previous relations such as the Ruse-Lanczos identity, the Bel-Matte decomposition and the Lovelock-like quadratic identities. We conclude pointing out some possible applications of the formalism.
Keywords
Cite
@article{arxiv.2311.14879,
title = {Remarks on the algebraic structure of (2, 2) double forms},
author = {E. Goulart and J. E. Ottoni},
journal= {arXiv preprint arXiv:2311.14879},
year = {2024}
}