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<p>On smooth manifolds of dimension <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(n \ge 4\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>n</mi> <mo>≥</mo> <mn>4</mn> </mrow> </math></EquationSource> </InlineEquation>, we prove that the torsion and curvature are, up to a scalar factor, the only pair of a vector-valued 2-form and an endomorphism-valued 2-form naturally associated with a linear connection that satisfy both the linear and differential Bianchi identities. This result extends to arbitrary linear connections a recent characterization of the curvature tensor of a symmetric linear connection obtained in Gordillo-Merino and Martínez-Bohórquez (Rev R Acad Cienc Exact Fis Nat Ser A Mat RACSAM 118(7):17, 2024).</p>

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Uniqueness of the Torsion–Curvature Pair

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年3月14日

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  • Raúl Martínez-Bohórquez,
  • José Navarro,
  • Juan B. Sancho

摘要

On smooth manifolds of dimension \(n \ge 4\) n ≥ 4 , we prove that the torsion and curvature are, up to a scalar factor, the only pair of a vector-valued 2-form and an endomorphism-valued 2-form naturally associated with a linear connection that satisfy both the linear and differential Bianchi identities. This result extends to arbitrary linear connections a recent characterization of the curvature tensor of a symmetric linear connection obtained in Gordillo-Merino and Martínez-Bohórquez (Rev R Acad Cienc Exact Fis Nat Ser A Mat RACSAM 118(7):17, 2024).