4维中由Kulkarni--Nomizu积构造的共形协变2-张量的分类
Classification of Conformally Covariant 2-Tensors from the Kulkarni--Nomizu Product in Dimension 4
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中文总结 AI 辅助
本文在4维中分类了由度量、Schouten张量、协变导数和Kulkarni-Nomizu积构造的共形协变对称(0,2)-张量，证明其空间为2维，由Bach张量和Eastwood-Singer张量张成，并用Lean 4和精确有理算术验证了代数与计算细节。
中文摘要 AI 辅助
我们在4维中分类了所有自然的、共形协变的、共形权为-2且微分阶数小于或等于4的对称(0,2)-张量，这些张量由度量、Schouten张量、协变导数以及Kulkarni-Nomizu积构造。我们证明了这类张量的空间恰好是2维的，由Bach张量（2阶）和Eastwood-Singer张量（4阶）张成。其代数核心使用Lean 4与Mathlib进行了形式化验证。8×11约束矩阵和无散度条件通过精确有理算术进行了计算验证。提供英文和俄文版本；俄文版本作为附件提供。
英文摘要
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.
发表机构
- Saint Petersburg State University（圣彼得堡国立大学）
机构由 AI 辅助整理，请以论文原文为准。
