PreprintCC BY 4.0arXiv
Classification of Conformally Covariant 2-Tensors from the Kulkarni--Nomizu Product in Dimension 4
Abstract
We classify all natural, conformally covariant, symmetric (0,2)-tensors of conformal weight -2 and differential order less than or equal to 4 in dimension 4, built from the metric, the Schouten tensor, covariant derivatives, and the Kulkarni-Nomizu product. We prove that the space of such tensors is exactly 2-dimensional, spanned by the Bach tensor (order 2) and the Eastwood-Singer tensor (order 4). The algebraic core is formally verified using Lean 4 with Mathlib. The 8x11 constraint matrix and divergence-free condition are verified computationally with exact rational arithmetic. Both English and Russian versions provided; Russian version available as ancillary.
Related
- Higher-dimensional full vertex algebras and systems of conformally covariant correlation functions
- Robust dimension-free estimation of simple random tensors: optimal guarantees under heavy tails and adversarial contamination
- Completing the classification of Hopf superalgebras of dimension up to 10
- The classification of some polynomial maps in dimension three
- Classification of cohomogeneity one steady gradient Ricci solitons in dimension four and five
BibTeX
@misc{berdinsky2026classification,
title = {{Classification of Conformally Covariant 2-Tensors from the Kulkarni--Nomizu Product in Dimension 4}},
author = {Yury N. Berdinsky},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.07750},
eprint = {2609.07750},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.07750},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Classification of Conformally Covariant 2-Tensors from the Kulkarni--Nomizu Product in Dimension 4
AU - Yury N. Berdinsky
PY - 2026
DA - 2026/09/07
PB - arXiv
DO - 10.48550/arxiv.2609.07750
UR - https://arxiv.org/abs/2609.07750
AB - We classify all natural, conformally covariant, symmetric (0,2)-tensors of conformal weight -2 and differential order less than or equal to 4 in dimension 4, built from the metric, the Schouten tensor, covariant derivatives, and the Kulkarni-Nomizu product. We prove that the space of such tensors is exactly 2-dimensional, spanned by the Bach tensor (order 2) and the Eastwood-Singer tensor (order 4). The algebraic core is formally verified using Lean 4 with Mathlib. The 8x11 constraint matrix and divergence-free condition are verified computationally with exact rational arithmetic. Both English and Russian versions provided; Russian version available as ancillary.
ER -