About: Riemannian geometry

Property	Value
rdf:type	skos:Concept
rdfs:label	Riemannian geometry
skos:broader	dbpedia:Category:Geometry dbpedia:Category:Differential_geometry dbpedia:Category:Metric_geometry
skos:prefLabel	Riemannian geometry
is skos:broader of	dbpedia:Category:Riemann_surfaces
is skos:subject of	dbpedia:Curvature dbpedia:Scalar_curvature dbpedia:Einstein_notation dbpedia:Covariant_derivative dbpedia:Riemann_curvature_tensor dbpedia:Hodge_dual dbpedia:Levi-Civita_connection dbpedia:Ricci_flow dbpedia:Tortuosity dbpedia:Almost_flat_manifold dbpedia:Barta's_theorem dbpedia:Fermi_coordinates dbpedia:Orthonormal_frame dbpedia:Bolza_surface dbpedia:Soul_theorem dbpedia:Calabi_flow dbpedia:Calibrated_geometry dbpedia:Cartan–Hadamard_theorem dbpedia:Cheng's_eigenvalue_comparison_theorem dbpedia:Conjugate_points dbpedia:De_Sitter–Schwarzschild dbpedia:Einstein_manifold dbpedia:Essential_manifold dbpedia:G2_manifold dbpedia:Gauss's_lemma_(Riemannian_geometry) dbpedia:Gauss_map dbpedia:Geodesic_deviation_equation dbpedia:Geometric_flow dbpedia:Hopf–Rinow_theorem dbpedia:Hyperkähler_manifold dbpedia:Isoparametric_manifold dbpedia:Lie_bracket_of_vector_fields dbpedia:Riemannian_geometry dbpedia:De_Sitter_space dbpedia:Metric_tensor dbpedia:Parallel_transport dbpedia:Christoffel_symbols dbpedia:Riemannian_manifold dbpedia:Beltrami's_theorem dbpedia:Berger–Kazdan_comparison_theorem dbpedia:Cotton_tensor dbpedia:Bonnet_theorem dbpedia:Covariance_and_contravariance_of_vectors dbpedia:Clifford_bundle dbpedia:Conformal_pictures dbpedia:Curvature_of_Riemannian_manifolds dbpedia:De_Sitter_invariant_special_relativity dbpedia:Filling_area_conjecture dbpedia:Fundamental_theorem_of_Riemannian_geometry dbpedia:Gromov's_compactness_theorem_(geometry) dbpedia:Gromov's_systolic_inequality_for_essential_manifolds dbpedia:Hitchin–Thorpe_inequality dbpedia:Hodge_theory dbpedia:Introduction_to_systolic_geometry dbpedia:Jacobi_field dbpedia:Kretschmann_scalar dbpedia:Minimal_volume dbpedia:Ricci_curvature dbpedia:Conformal_map dbpedia:Nash_embedding_theorem dbpedia:Geodesic_curvature dbpedia:Geometrization_conjecture dbpedia:Kähler_manifold dbpedia:Normal_coordinates dbpedia:Theorema_Egregium dbpedia:Second_fundamental_form dbpedia:Abel–Jacobi_map dbpedia:Exponential_map dbpedia:Berger's_sphere dbpedia:Cheeger_constant dbpedia:Christoffel_symbols/Proofs dbpedia:Conformally_flat_manifold dbpedia:Filling_radius dbpedia:First_variation_of_area_formula dbpedia:G2-structure dbpedia:Geodesic_convexity dbpedia:Geodesic_manifold dbpedia:Glossary_of_Riemannian_and_metric_geometry dbpedia:Harmonic_map dbpedia:Hermitian_manifold dbpedia:Line_element dbpedia:Musical_isomorphism dbpedia:Systolic_geometry dbpedia:Geodesic dbpedia:Gromov–Hausdorff_convergence dbpedia:Holonomy dbpedia:Killing_vector_field dbpedia:2π_theorem dbpedia:Bishop–Gromov_inequality dbpedia:Bryant_surface dbpedia:Cartan–Karlhede_algorithm dbpedia:Collapsing_manifold dbpedia:Comparison_theorem dbpedia:Constant_curvature dbpedia:Constraint_counting dbpedia:Curved_space dbpedia:Cut_locus_(Riemannian_manifold) dbpedia:Flat_manifold dbpedia:Gauss–Codazzi_equations dbpedia:Geodesics_as_Hamiltonian_flows dbpedia:Gravitational_instanton dbpedia:Gromov's_inequality_for_complex_projective_space dbpedia:Hermitian_symmetric_space dbpedia:Isometry_(Riemannian_geometry) dbpedia:Laplace–Beltrami_operator dbpedia:Lichnerowicz_formula dbpedia:List_of_formulas_in_Riemannian_geometry dbpedia:Loewner's_torus_inequality dbpedia:Metric_connection dbpedia:Myers's_theorem dbpedia:Nuts_and_bolts_(general_relativity) dbpedia:Pu's_inequality dbpedia:Quaternion-Kähler_symmetric_space dbpedia:Riemannian_submanifold dbpedia:Riemannian_submersion dbpedia:Ruppeiner_geometry dbpedia:Sasakian_manifold dbpedia:Space_form dbpedia:Sphere_theorem dbpedia:Spherical_3-manifold dbpedia:Splitting_theorem dbpedia:Sub-Riemannian_manifold dbpedia:Symmetric_space dbpedia:Synge's_theorem dbpedia:Thurston_elliptization_conjecture dbpedia:Weyl_tensor dbpedia:Weyl–Schouten_theorem dbpedia:Poincaré_metric dbpedia:Prescribed_Ricci_curvature_problem dbpedia:Pseudo-Riemannian_manifold dbpedia:Quaternion-Kähler_manifold dbpedia:Riemannian_circle dbpedia:Smooth_coarea_formula dbpedia:Spectral_geometry dbpedia:Spin(7)-manifold dbpedia:Uniformization_theorem dbpedia:Toponogov's_theorem dbpedia:Total_curvature dbpedia:Prescribed_scalar_curvature_problem dbpedia:Ricci_decomposition dbpedia:Schur's_lemma_(from_Riemannian_geometry) dbpedia:Spin_structure dbpedia:Systoles_of_surfaces dbpedia:Unit_tangent_bundle dbpedia:Wiedersehen_pair dbpedia:Yamabe_flow dbpedia:Ricci-flat_manifold dbpedia:Riemannian_Penrose_inequality dbpedia:Schouten_tensor dbpedia:Sectional_curvature dbpedia:Seifert-Weber_space dbpedia:Vector_flow dbpedia:Weakly_symmetric_space