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- Calibrated_geometry abstract "In the mathematical field of differential geometry, a calibrated manifold is a Riemannian manifold (M,g) of dimension n equipped with a differential p-form φ (for some 0 ≤ p ≤ n) which is a calibration in the sense that φ is closed: dφ = 0, where d is the exterior derivative for any x ∈ M and any oriented p-dimensional subspace ξ of TxM, φ|ξ = λ volξ with λ ≤ 1. Here volξ is the volume form of ξ with respect to g.Set Gx(φ) = { ξ as above : φ|ξ = volξ }. (In order for the theory to be nontrivial, we need Gx(φ) to be nonempty.) Let G(φ) be the union of Gx(φ) for x in M.The theory of calibrations is due to R. Harvey and B. Lawson and others. Much earlier (in 1966) Edmond Bonan introduced G2-manifold and Spin(7)-manifold, constructed all the parallel forms and showed that those manifolds were Ricci-flat. Quaternion-Kähler manifold were simultaneously studied in 1965 by Edmond Bonan and Vivian Yoh Kraines and they constructed the parallel 4-form.".
- Calibrated_geometry wikiPageID "19364294".
- Calibrated_geometry wikiPageRevisionID "599499656".
- Calibrated_geometry hasPhotoCollection Calibrated_geometry.
- Calibrated_geometry subject Category:Differential_geometry.
- Calibrated_geometry subject Category:Riemannian_geometry.
- Calibrated_geometry subject Category:Structures_on_manifolds.
- Calibrated_geometry type Artifact100021939.
- Calibrated_geometry type Object100002684.
- Calibrated_geometry type PhysicalEntity100001930.
- Calibrated_geometry type Structure104341686.
- Calibrated_geometry type StructuresOnManifolds.
- Calibrated_geometry type Whole100003553.
- Calibrated_geometry type YagoGeoEntity.
- Calibrated_geometry type YagoPermanentlyLocatedEntity.
- Calibrated_geometry comment "In the mathematical field of differential geometry, a calibrated manifold is a Riemannian manifold (M,g) of dimension n equipped with a differential p-form φ (for some 0 ≤ p ≤ n) which is a calibration in the sense that φ is closed: dφ = 0, where d is the exterior derivative for any x ∈ M and any oriented p-dimensional subspace ξ of TxM, φ|ξ = λ volξ with λ ≤ 1. Here volξ is the volume form of ξ with respect to g.Set Gx(φ) = { ξ as above : φ|ξ = volξ }.".
- Calibrated_geometry label "Calibrated geometry".
- Calibrated_geometry sameAs 측정기하학.
- Calibrated_geometry sameAs m.04n259k.
- Calibrated_geometry sameAs Q5019833.
- Calibrated_geometry sameAs Q5019833.
- Calibrated_geometry sameAs Calibrated_geometry.
- Calibrated_geometry wasDerivedFrom Calibrated_geometry?oldid=599499656.
- Calibrated_geometry isPrimaryTopicOf Calibrated_geometry.