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Scalar curvatureRiemann surfaceRiemannian geometryRicci-flat manifoldDifferential geometry of surfacesTangent spaceEuclidean topologyRicci curvatureHyperbolic spaceCurvature formRiemann curvature tensorEinstein tensorDirac equation in curved spacetimeEuler's theoremGaussian curvatureSpin structureTangent coneRiemannian manifoldLebesgue covering dimensionGeometric topologyHausdorff measureStein manifoldCauchy surfaceSoul theoremPseudo-riemannian manifoldDistortionCurvilinear coordinatesDifferentiable curveGeometric multiplicityExponential mapRiesz transformDifferential formSymplectic geometryCotangent bundleTorsion of a curveCausal structureQuadricGeometric measure theoryCurvatureDifferential topologyTopological manifoldRicci flowCalculus on euclidean spaceCodimensionDivisorRiemann spaceHarnack's curve theoremSymplectic manifoldMinkowski spaceMean curvature flowSymmetric spaceGeodesicCalabi-yau manifoldCongruenceGeometry of numbersCartan connectionEinstein spaceEuler classConic constantCovariant derivativeRadius of curvatureGaussian measurePrincipal curvatureDegree of a field extensionRegge calculusDifferential geometryCartan decompositionOutline of geometryFractal derivativePseudo-euclidean spaceConformal symmetryExterior derivativeOsculating planeLow-dimensional topologyDimensionComplex geometryMetric tensorTangent-secant theoremTorsion tensorCoarea formulaConformal geometryLinking numberSymplectic vector spaceCurveHigher-dimensional algebraStatistical manifoldDistributionIntegral curveCoordinate systemSectionSpacetimeMetrizable spaceSection modulusMapping class groupHarmonic mapGeometric flowFractalLength of a moduleConic sectionDifferential structure