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Riemannian geometryRiemann surfaceRicci-flat manifoldRicci flowRiemann sphereNash embedding theoremsSchanuel's conjectureCalabi-yau manifoldRiemann hypothesisRiemannian manifoldHermitian manifoldDifferential geometry of surfacesHarmonic mapComplex differential formCauchy surfaceComplex geometryEuler's theoremDirichlet's approximation theoremStein manifoldScalar curvatureSoul theoremGeometric topologyAdjunction formulaEuclidean topologySectional curvatureTheorema egregiumK-stabilityHarnack's curve theoremRicci curvatureComplex torusSymplectic manifoldEinstein spaceRiemann spaceQuasiconformal mappingStatistical manifoldMusical isomorphismHurewicz theoremMorera's theoremSchwarz lemmaGeneralized riemann hypothesisCoherent sheafClosed-subgroup theoremLefschetz hyperplane theoremComplex projective spaceRiemann xi functionGeometrization conjectureComplex lie groupCauchy's integral theoremRiemann integralContact geometryDirac equation in curved spacetimeExterior algebraCongruenceHodge conjectureRicci calculusHermitian connectionAlmost complex manifoldSerre dualityDifferential topologyCotangent complexGeometric flowCantor spaceIsometryMatiyasevich's theoremBelyi's theoremKoszul complexHypercomplex analysisRiemann curvature tensorRiemann sumCartan decompositionMetrizable spaceTangent spaceResolvent formalismGauss-bonnet theoremSimons' formulaMultiple zeta functionSymplectic geometryRamanujan primeRiemann-stieltjes integralRunge's theoremHolomorphic vector bundleOpen book decompositionLefschetz fixed-point theoremContour integrationCalculus on euclidean spaceTopological manifoldTangent coneExponential mapMean curvature flowGrassmannianCauchy's integral formulaHodge theoryLorentz spaceGeometric measure theoryMiquel's theoremCotangent bundleK3 surfaceArithmetic geometryFisher information metricLinking number