| dbo:abstract |
Els tensors de Codazzi (així anomenats pel seu descobridor, Delfino Codazzi) apareixen de manera natural en l'estudi de les varietats riemannianes amb curvatura harmònica o tensor de Weyl harmonic. De fet, l'existència de tensors de Codazzi imposa condicions estrictes al tensor de curvatura de la varietat. (ca) In the mathematical field of differential geometry, a Codazzi tensor (named after Delfino Codazzi) is a symmetric 2-tensor whose covariant derivative is also symmetric. Such tensors arise naturally in the study of Riemannian manifolds with harmonic curvature or harmonic Weyl tensor. In fact, existence of Codazzi tensors impose strict conditions on the curvature tensor of the manifold. Also, the second fundamental form of an immersed hypersurface in a space form (relative to a local choice of normal field) is a Codazzi tensor. (en) |
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dbr:Riemannian_manifolds dbr:Levi-Civita_connection dbr:Delfino_Codazzi dbr:Harmonic dbr:Weyl–Schouten_theorem dbr:Curvature dbr:Riemann_curvature_tensor dbr:Covariant_derivative dbr:Tensor dbc:Tensors dbr:Differential_geometry dbr:Space_form dbr:Weyl_tensor dbr:Weyl_curvature_tensor |
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| rdfs:comment |
Els tensors de Codazzi (així anomenats pel seu descobridor, Delfino Codazzi) apareixen de manera natural en l'estudi de les varietats riemannianes amb curvatura harmònica o tensor de Weyl harmonic. De fet, l'existència de tensors de Codazzi imposa condicions estrictes al tensor de curvatura de la varietat. (ca) In the mathematical field of differential geometry, a Codazzi tensor (named after Delfino Codazzi) is a symmetric 2-tensor whose covariant derivative is also symmetric. Such tensors arise naturally in the study of Riemannian manifolds with harmonic curvature or harmonic Weyl tensor. In fact, existence of Codazzi tensors impose strict conditions on the curvature tensor of the manifold. Also, the second fundamental form of an immersed hypersurface in a space form (relative to a local choice of normal field) is a Codazzi tensor. (en) |
| rdfs:label |
Tensor de Codazzi (ca) Codazzi tensor (en) |
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freebase:Codazzi tensor yago-res:Codazzi tensor wikidata:Codazzi tensor dbpedia-ca:Codazzi tensor https://global.dbpedia.org/id/4i3Xj |
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dbr:Beltrami's_theorem dbr:Delfino_Codazzi dbr:Weyl–Schouten_theorem |
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wikipedia-en:Codazzi_tensor |