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Riemannian geometryCalabi conjectureGeometric topologySymmetric spaceEuclidean topologyCantor spaceExponential mapGeometric flowCayley's theoremStein manifoldSoul theoremMetrizable spaceRiemann surfaceDifferential geometry of surfacesIsomorphism theoremsSymplectic manifoldEuler's theoremMusical isomorphismRicci-flat manifoldGeometrization conjectureTietze extension theoremRicci flowTopological manifoldCotangent bundleTangent spaceEuclidean groupHermitian manifoldSymplectic geometryHurewicz theoremHilbert spaceIsometrySectional curvatureAffine groupStatistical manifoldSpin structureRigid transformationPseudo-riemannian manifoldEinstein tensorHarmonic mapRiemann sphereHopf fibrationOsculating planeMinkowski spaceGravitational instantonConformally flat manifoldEuclidean domainCalculus on euclidean spaceRiemannian manifoldInvariant manifoldIsometry groupLevi-civita connectionHyperbolic spaceLefschetz hyperplane theoremCantor's intersection theoremFisher information metricHodge theoryManifoldToric varietyRicci curvatureNuclear spaceIsogenyKepler conjectureDirac equation in curved spacetimeSimons' formulaCongruenceDirichlet's approximation theoremHolomorphic vector bundleRepresentation theoremLocal diffeomorphismHyperplane separation theoremDarboux's theoremGeodesicEuclidean plane isometryMeasurable functionLie's third theoremRegular measureJordan curve theoremNewton fractalCoarea formulaLefschetz fixed-point theoremSegre embeddingHomeomorphismSubmanifoldMetric tensorSchur's lemmaClosed graph theoremTheorema egregiumTychonoff's theoremFundamental polygonMean curvature flowCodimensionBounded inverse theoremSimple homotopy theoryGeometric measure theoryCauchy surfaceOrbifoldDifferential formPseudo-euclidean spaceConvex conjugateHausdorff measure