fundamental_theorem_of_riemannian_geometry.pdf

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Math230a (Fall 2025) Yum-Tong Siu 1 Fundamental Theorem of Riemannian Geometry Earlier we discussed connections for a smooth vector bundle V of rank over a smooth manifold X of real dimension n. Such connections are arti- ficially introduced by specifying the total covariant differentiation of a local frame e1 , · · · , er to be X n Deα = ωαβ eβ , β=1 where ω = (ωαβ )1≤α,β≤ris an r × r matrix whose entries are…

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