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Ricci curvatureRiemann curvature tensorEinstein field equationTensor calculusEinstein spaceRiemannian geometryDirac equation in curved spacetimeMetric tensorEuler's theoremRicci calculusRicci-flat manifoldRicci flowSectional curvatureDifferential geometry of surfacesElectromagnetic tensorRiemannian manifoldScalar curvatureEinstein field equationsRiemann spaceErnst equationExponential mapEuclidean topologyGeneral relativityTensor fieldDifferentiable curveGeometric flowDifferential formCurvature formSpin structureCartesian tensorLorentz transformationCalabi-yau manifoldEuler's formulaExterior covariant derivativeRegge calculusPseudo-riemannian manifoldDarboux's theoremCotangent bundleTensor densityWeyl tensorRelativistic lagrangian mechanicsLie derivativeGeometric topologySymplectic manifoldGauge theoryTangent spaceMusical isomorphismTorsion tensorTorsion of a curveLinearized gravityLaplace operatorStructure tensorEuler classMean curvature flowDifferential topologySymplectic geometryGauss mapDifferential geometrySecond fundamental formCovariant derivativeCausal structureLevi-civita connectionCongruencePost-newtonian expansionGeometrodynamicsTheorema egregiumMean curvaturePetrov classificationEinstein notationStrain-rate tensorGaussian curvatureInversive geometryGauge covariant derivativeTensor operatorSpacetimeTensor algebraSymmetric spaceGauss-bonnet theoremStein manifoldLorentz groupLegendre transformationCalculus on euclidean spaceAffine connectionRiemann surfaceSchmidt decompositionHessian matrixFractal derivativeDistributionGeometric measure theoryLaplace-beltrami operatorCartan connectionTangent conePseudodifferential operatorGravitational instantonGeodesicSimons' formulaPseudo-euclidean spaceGeometric analysisVector fieldMeasure theory