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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 wikiPageLength "7622".
- Calibrated_geometry wikiPageOutDegree "21".
- Calibrated_geometry wikiPageRevisionID "675425331".
- Calibrated_geometry wikiPageWikiLink Calabi–Yau_manifold.
- Calibrated_geometry wikiPageWikiLink Category:Differential_geometry.
- Calibrated_geometry wikiPageWikiLink Category:Riemannian_geometry.
- Calibrated_geometry wikiPageWikiLink Category:Structures_on_manifolds.
- Calibrated_geometry wikiPageWikiLink Complex_manifold.
- Calibrated_geometry wikiPageWikiLink Complex_submanifold.
- Calibrated_geometry wikiPageWikiLink Differential_form.
- Calibrated_geometry wikiPageWikiLink Differential_geometry.
- Calibrated_geometry wikiPageWikiLink Edmond_Bonan.
- Calibrated_geometry wikiPageWikiLink Exterior_derivative.
- Calibrated_geometry wikiPageWikiLink G2_manifold.
- Calibrated_geometry wikiPageWikiLink Kähler_form.
- Calibrated_geometry wikiPageWikiLink Kähler_manifold.
- Calibrated_geometry wikiPageWikiLink Mathematics.
- Calibrated_geometry wikiPageWikiLink Quaternion-Kähler_manifold.
- Calibrated_geometry wikiPageWikiLink Riemannian_manifold.
- Calibrated_geometry wikiPageWikiLink Special_Lagrangian_submanifold.
- Calibrated_geometry wikiPageWikiLink Spin(7)-manifold.
- Calibrated_geometry wikiPageWikiLink Stokes_theorem.
- Calibrated_geometry wikiPageWikiLink Symplectic_manifold.
- Calibrated_geometry wikiPageWikiLinkText "Calibrated geometry".
- Calibrated_geometry wikiPageWikiLinkText "calibrated geometry".
- Calibrated_geometry wikiPageWikiLinkText "calibration".
- Calibrated_geometry wikiPageWikiLinkText "calibrations in the sense of Harvey–Lawson".
- Calibrated_geometry wikiPageWikiLinkText "calibrations".
- Calibrated_geometry hasPhotoCollection Calibrated_geometry.
- Calibrated_geometry wikiPageUsesTemplate Template:Citation.
- Calibrated_geometry subject Category:Differential_geometry.
- Calibrated_geometry subject Category:Riemannian_geometry.
- Calibrated_geometry subject Category:Structures_on_manifolds.
- Calibrated_geometry hypernym Manifold.
- Calibrated_geometry type Physic.
- 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 wasDerivedFrom Calibrated_geometry?oldid=675425331.
- Calibrated_geometry isPrimaryTopicOf Calibrated_geometry.