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Riemann surfaceHermitian connectionManifoldHilbert manifoldGeometric topologyAnalytic manifoldComplex lie groupComplex differential formRicci-flat manifoldTopological manifoldAlmost complex manifoldProper morphismComplex geometryComplex projective spaceMetrizable spaceDifferential topologyStein manifoldSymplectic manifoldDifferential geometry of surfacesTangent coneFinsler manifoldHolomorphic vector bundleRiemannian geometryLie groupStatistical manifoldDifferentiable manifoldDiffeomorphismMorse homologyScalar curvatureSymplectomorphismPiecewise linear manifoldCotangent complexCauchy surfaceSpectral spaceSymplectic geometryInvariant manifoldCoherent sheafSurfaceHomotopy theoryLocal diffeomorphismComplex torusComplex logarithmCovariant derivativeSimple homotopy theoryEuclidean topologyOrbifoldMinkowski spaceSymmetric spaceCotangent bundleDifferential geometryHarmonic mapSectional curvatureAlgebraic integerTangent spaceClosed manifoldHermite normal formSimplicial homologyHypercomplex analysisCongruenceHomological algebraConnectionExponential mapHodge theoryTangent bundleK-stabilitySimplicial complexCausal structureTopological propertyCompact-open topologyHyperbolic manifoldHamiltonian vector fieldSpin structureDifferential formSymplectic integratorHyperbolic functionsConfiguration spaceSubmanifoldEuler classAlgebra homomorphismConnected sumMorse theoryExponential sheaf sequenceDifferential invariantHolomorphic functionCartan connectionGeodesic curvatureAlgebraic topologyConvex geometryKleinian groupProjective geometryCellular homologyIsometryGravitational instantonExterior derivativeGeodesicRiemann sumHomotopy groupQuadricGeometric measure theoryRiemannian manifold