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- Ricci-flat_manifold abstract "In mathematics, Ricci-flat manifolds are Riemannian manifolds whose Ricci curvature vanishes. In physics, they represent vacuum solutions to the analogues of Einstein's equations for Riemannian manifolds of any dimension, with vanishing cosmological constant. Ricci-flat manifolds are special cases of Einstein manifolds, where the cosmological constant need not vanish.Since Ricci curvature measures the amount by which the volume of a small geodesic ball deviates from the volume of a ball in Euclidean space, small geodesic balls will have no volume deviation, but their "shape" may vary from the shape of the standard ball in Euclidean space. For example, in a Ricci-flat manifold, a circle in Euclidean space may be deformed into an ellipse with equal area. This is due to Weyl curvature.Ricci-flat manifolds often have restricted holonomy groups. Important cases include Calabi–Yau manifolds and hyperkähler manifolds.".
- Ricci-flat_manifold wikiPageID "644797".
- Ricci-flat_manifold wikiPageLength "1662".
- Ricci-flat_manifold wikiPageOutDegree "17".
- Ricci-flat_manifold wikiPageRevisionID "654262787".
- Ricci-flat_manifold wikiPageWikiLink Calabi–Yau_manifold.
- Ricci-flat_manifold wikiPageWikiLink Category:Riemannian_manifolds.
- Ricci-flat_manifold wikiPageWikiLink Cosmological_constant.
- Ricci-flat_manifold wikiPageWikiLink Einstein_field_equations.
- Ricci-flat_manifold wikiPageWikiLink Einstein_manifold.
- Ricci-flat_manifold wikiPageWikiLink Einsteins_equations.
- Ricci-flat_manifold wikiPageWikiLink Euclidean_space.
- Ricci-flat_manifold wikiPageWikiLink Flat_manifold.
- Ricci-flat_manifold wikiPageWikiLink Holonomy.
- Ricci-flat_manifold wikiPageWikiLink Holonomy_group.
- Ricci-flat_manifold wikiPageWikiLink Hyperkähler_manifold.
- Ricci-flat_manifold wikiPageWikiLink Mathematics.
- Ricci-flat_manifold wikiPageWikiLink Physics.
- Ricci-flat_manifold wikiPageWikiLink Quaternion-Kähler_manifold.
- Ricci-flat_manifold wikiPageWikiLink Ricci_curvature.
- Ricci-flat_manifold wikiPageWikiLink Riemannian_manifold.
- Ricci-flat_manifold wikiPageWikiLink Vacuum_solution.
- Ricci-flat_manifold wikiPageWikiLink Weyl_curvature.
- Ricci-flat_manifold wikiPageWikiLink Weyl_tensor.
- Ricci-flat_manifold wikiPageWikiLinkText "Ricci flat".
- Ricci-flat_manifold wikiPageWikiLinkText "Ricci-flat manifold".
- Ricci-flat_manifold wikiPageWikiLinkText "Ricci-flat spaces".
- Ricci-flat_manifold wikiPageWikiLinkText "Ricci-flat".
- Ricci-flat_manifold wikiPageWikiLinkText "Ricci-flat_manifold".
- Ricci-flat_manifold hasPhotoCollection Ricci-flat_manifold.
- Ricci-flat_manifold wikiPageUsesTemplate Template:Differential-geometry-stub.
- Ricci-flat_manifold wikiPageUsesTemplate Template:Reflist.
- Ricci-flat_manifold subject Category:Riemannian_manifolds.
- Ricci-flat_manifold hypernym Manifolds.
- Ricci-flat_manifold comment "In mathematics, Ricci-flat manifolds are Riemannian manifolds whose Ricci curvature vanishes. In physics, they represent vacuum solutions to the analogues of Einstein's equations for Riemannian manifolds of any dimension, with vanishing cosmological constant.".
- Ricci-flat_manifold label "Ricci-flat manifold".
- Ricci-flat_manifold sameAs リッチ平坦多様体.
- Ricci-flat_manifold sameAs m.02_1p8.
- Ricci-flat_manifold sameAs Q7322952.
- Ricci-flat_manifold sameAs Q7322952.
- Ricci-flat_manifold sameAs 里奇平坦流形.
- Ricci-flat_manifold wasDerivedFrom Ricci-flat_manifold?oldid=654262787.
- Ricci-flat_manifold isPrimaryTopicOf Ricci-flat_manifold.