Matches in DBpedia 2015-10 for { <http://dbpedia.org/resource/Ricci_curvature> ?p ?o }
- Ricci_curvature abstract "In differential geometry, the Ricci curvature tensor, named after Gregorio Ricci-Curbastro, represents the amount by which the volume of a geodesic ball in a curved Riemannian manifold deviates from that of the standard ball in Euclidean space. As such, it provides one way of measuring the degree to which the geometry determined by a given Riemannian metric might differ from that of ordinary Euclidean n-space. The Ricci tensor is defined on any pseudo-Riemannian manifold, as a trace of the Riemann curvature tensor. Like the metric itself, the Ricci tensor is a symmetric bilinear form on the tangent space of the manifold (Besse 1987, p. 43).In relativity theory, the Ricci tensor is the part of the curvature of space-time that determines the degree to which matter will tend to converge or diverge in time (via the Raychaudhuri equation). It is related to the matter content of the universe by means of the Einstein field equation. In differential geometry, lower bounds on the Ricci tensor on a Riemannian manifold allow one to extract global geometric and topological information by comparison (cf. comparison theorem) with the geometry of a constant curvature space form. If the Ricci tensor satisfies the vacuum Einstein equation, then the manifold is an Einstein manifold, which have been extensively studied (cf. Besse 1987). In this connection, the Ricci flow equation governs the evolution of a given metric to an Einstein metric; the precise manner in which this occurs ultimately leads to the solution of the Poincaré conjecture.".
- Ricci_curvature wikiPageExternalLink 0606774.
- Ricci_curvature wikiPageExternalLink 0612107.
- Ricci_curvature wikiPageID "276582".
- Ricci_curvature wikiPageLength "20529".
- Ricci_curvature wikiPageOutDegree "108".
- Ricci_curvature wikiPageRevisionID "677223167".
- Ricci_curvature wikiPageWikiLink Affine_connection.
- Ricci_curvature wikiPageWikiLink Annals_of_Mathematics.
- Ricci_curvature wikiPageWikiLink Ball_(mathematics).
- Ricci_curvature wikiPageWikiLink Basic_introduction_to_the_mathematics_of_curved_spacetime.
- Ricci_curvature wikiPageWikiLink Bianchi_identities.
- Ricci_curvature wikiPageWikiLink Bishop–Gromov_inequality.
- Ricci_curvature wikiPageWikiLink Cambridge_University_Press.
- Ricci_curvature wikiPageWikiLink Canonical_bundle.
- Ricci_curvature wikiPageWikiLink Category:Curvature_(mathematics).
- Ricci_curvature wikiPageWikiLink Category:Riemannian_geometry.
- Ricci_curvature wikiPageWikiLink Category:Tensors_in_general_relativity.
- Ricci_curvature wikiPageWikiLink Chern_class.
- Ricci_curvature wikiPageWikiLink Christina_Sormani.
- Ricci_curvature wikiPageWikiLink Christoffel_symbols.
- Ricci_curvature wikiPageWikiLink Closed_and_exact_differential_forms.
- Ricci_curvature wikiPageWikiLink Closed_and_exact_forms.
- Ricci_curvature wikiPageWikiLink Cohomology.
- Ricci_curvature wikiPageWikiLink Cohomology_class.
- Ricci_curvature wikiPageWikiLink Comparison_theorem.
- Ricci_curvature wikiPageWikiLink Complex_differential_form.
- Ricci_curvature wikiPageWikiLink Complex_manifold.
- Ricci_curvature wikiPageWikiLink Cosmological_constant.
- Ricci_curvature wikiPageWikiLink Curvature_form.
- Ricci_curvature wikiPageWikiLink Curvature_of_Riemannian_manifolds.
- Ricci_curvature wikiPageWikiLink Curvature_of_space-time.
- Ricci_curvature wikiPageWikiLink Determinant.
- Ricci_curvature wikiPageWikiLink Differential_geometry.
- Ricci_curvature wikiPageWikiLink Dolbeault_operator.
- Ricci_curvature wikiPageWikiLink Einstein_field_equation.
- Ricci_curvature wikiPageWikiLink Einstein_field_equations.
- Ricci_curvature wikiPageWikiLink Einstein_manifold.
- Ricci_curvature wikiPageWikiLink Einstein_notation.
- Ricci_curvature wikiPageWikiLink Einstein_summation_convention.
- Ricci_curvature wikiPageWikiLink Euclidean_space.
- Ricci_curvature wikiPageWikiLink Exterior_algebra.
- Ricci_curvature wikiPageWikiLink Exterior_power.
- Ricci_curvature wikiPageWikiLink Foundations_of_Differential_Geometry.
- Ricci_curvature wikiPageWikiLink Fundamental_group.
- Ricci_curvature wikiPageWikiLink G-structure.
- Ricci_curvature wikiPageWikiLink Gauss–Codazzi_equations.
- Ricci_curvature wikiPageWikiLink General_relativity.
- Ricci_curvature wikiPageWikiLink Geodesic.
- Ricci_curvature wikiPageWikiLink Geodesic_normal_coordinates.
- Ricci_curvature wikiPageWikiLink Gregorio_Ricci-Curbastro.
- Ricci_curvature wikiPageWikiLink Grigori_Perelman.
- Ricci_curvature wikiPageWikiLink Gromovs_compactness_theorem_(geometry).
- Ricci_curvature wikiPageWikiLink Harmonic_coordinates.
- Ricci_curvature wikiPageWikiLink Harmonic_function.
- Ricci_curvature wikiPageWikiLink Heat_equation.
- Ricci_curvature wikiPageWikiLink Holonomy.
- Ricci_curvature wikiPageWikiLink Homotopy.
- Ricci_curvature wikiPageWikiLink Homotopy_class.
- Ricci_curvature wikiPageWikiLink Hypersurface.
- Ricci_curvature wikiPageWikiLink Introduction_to_the_mathematics_of_general_relativity.
- Ricci_curvature wikiPageWikiLink Isometry.
- Ricci_curvature wikiPageWikiLink Jacobi_field.
- Ricci_curvature wikiPageWikiLink John_Wiley_&_Sons.
- Ricci_curvature wikiPageWikiLink Kähler_differential.
- Ricci_curvature wikiPageWikiLink Kähler_manifold.
- Ricci_curvature wikiPageWikiLink Laplace_operator.
- Ricci_curvature wikiPageWikiLink Laplace–Beltrami_operator.
- Ricci_curvature wikiPageWikiLink Laplacian.
- Ricci_curvature wikiPageWikiLink Levi-Civita_connection.
- Ricci_curvature wikiPageWikiLink Local_coordinates.
- Ricci_curvature wikiPageWikiLink Metric_tensor.
- Ricci_curvature wikiPageWikiLink Myers_theorem.
- Ricci_curvature wikiPageWikiLink Myerss_theorem.
- Ricci_curvature wikiPageWikiLink Normal_coordinates.
- Ricci_curvature wikiPageWikiLink Poincaré_conjecture.
- Ricci_curvature wikiPageWikiLink Principal_axis_theorem.
- Ricci_curvature wikiPageWikiLink Principal_curvature.
- Ricci_curvature wikiPageWikiLink Projective_differential_geometry.
- Ricci_curvature wikiPageWikiLink Pseudo-Riemannian_manifold.
- Ricci_curvature wikiPageWikiLink Raychaudhuri_equation.
- Ricci_curvature wikiPageWikiLink Relativity_theory.
- Ricci_curvature wikiPageWikiLink Ricci-flat_manifold.
- Ricci_curvature wikiPageWikiLink Ricci_calculus.
- Ricci_curvature wikiPageWikiLink Ricci_decomposition.
- Ricci_curvature wikiPageWikiLink Ricci_flow.
- Ricci_curvature wikiPageWikiLink Richard_Hamilton_(mathematician).
- Ricci_curvature wikiPageWikiLink Richard_Hamilton_(professor).
- Ricci_curvature wikiPageWikiLink Riemann_curvature_tensor.
- Ricci_curvature wikiPageWikiLink Riemannian_curvature_tensor.
- Ricci_curvature wikiPageWikiLink Riemannian_geometry.
- Ricci_curvature wikiPageWikiLink Riemannian_manifold.
- Ricci_curvature wikiPageWikiLink Riemannian_metric.
- Ricci_curvature wikiPageWikiLink Scalar_curvature.
- Ricci_curvature wikiPageWikiLink Second_fundamental_form.
- Ricci_curvature wikiPageWikiLink Sectional_curvature.
- Ricci_curvature wikiPageWikiLink Solution_of_the_Poincaré_conjecture.
- Ricci_curvature wikiPageWikiLink Space_form.
- Ricci_curvature wikiPageWikiLink Spherical_wedge.
- Ricci_curvature wikiPageWikiLink Splitting_theorem.