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- In der Mathematik ist der Satz von Cartan-Ambrose-Hicks ein Lehrsatz der Riemannschen Geometrie, dem zufolge Riemannsche Metriken lokal bereits durch den Riemannschen Krümmungstensor eindeutig festgelegt sind. Der Satz ist nach Élie Cartan benannt, der die lokale Version bewies, und Warren Ambrose und dessen Doktoranden Noel Hicks. Ambrose bewies 1956 eine globale Version. (de)
- In mathematics, the Cartan–Ambrose–Hicks theorem is a theorem of Riemannian geometry, according to which the Riemannian metric is locally determined by the Riemann curvature tensor, or in other words, behavior of the curvature tensor under parallel translation determines the metric. The theorem is named after Élie Cartan, Warren Ambrose, and his PhD student Noel Hicks. Cartan proved the local version. Ambrose proved a global version that allows for isometries between general Riemannian manifolds with varying curvature, in 1956. This was further generalized by Hicks to general manifolds with affine connections in their tangent bundles, in 1959. A statement and proof of the theorem can be found in (en)
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- 7652 (xsd:nonNegativeInteger)
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- In der Mathematik ist der Satz von Cartan-Ambrose-Hicks ein Lehrsatz der Riemannschen Geometrie, dem zufolge Riemannsche Metriken lokal bereits durch den Riemannschen Krümmungstensor eindeutig festgelegt sind. Der Satz ist nach Élie Cartan benannt, der die lokale Version bewies, und Warren Ambrose und dessen Doktoranden Noel Hicks. Ambrose bewies 1956 eine globale Version. (de)
- In mathematics, the Cartan–Ambrose–Hicks theorem is a theorem of Riemannian geometry, according to which the Riemannian metric is locally determined by the Riemann curvature tensor, or in other words, behavior of the curvature tensor under parallel translation determines the metric. A statement and proof of the theorem can be found in (en)
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- Satz von Cartan-Ambrose-Hicks (de)
- Cartan–Ambrose–Hicks theorem (en)
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