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This talk begins with examples of rigid and non-rigid geometric structures, followed by an in-depth discussion of the Fundamental Theorem of Riemannian Geometry, on existence and uniqueness of a torsion-free connection compatible with a Riemannian metric. This result is interpreted as giving a framing on the orthonormal frame bundle uniquely determined by the metric. It is seen to be a consequence of the vanishing of the first prolongation of the orthogonal Lie algebra.[-]
This talk begins with examples of rigid and non-rigid geometric structures, followed by an in-depth discussion of the Fundamental Theorem of Riemannian Geometry, on existence and uniqueness of a torsion-free connection compatible with a Riemannian metric. This result is interpreted as giving a framing on the orthonormal frame bundle uniquely determined by the metric. It is seen to be a consequence of the vanishing of the first prolongation of ...[+]

53B20 ; 53B05 ; 22F05

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