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R. Kulkarni (1972)
On the Bianchi identitiesMathematische Annalen, 199
Memoria Levi-Civita (1916)
Nozione di parallelismo in una varietà qualunque e conseguente specificazione geometrica della curvatura riemannianaRendiconti del Circolo Matematico di Palermo (1884-1940), 42
K. Nomizu (1954)
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H. Osborn (1967)
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D. Eisenbud (1995)
Modules of Differentials
Affine connections of 1-forms, rather than vector fields, induce complexes that project to the de Rham complexes of the underlying manifolds. This observation provides short direct proofs of Bianchi identities, existence and uniqueness of Levi-Civita connections, and symmetries of the Riemann curvature tensor.
Acta Applicandae Mathematicae – Springer Journals
Published: Oct 16, 2004
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