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ConnectionConnectorMetric tensorCotangent bundleIsometryExterior covariant derivativeMusical isomorphismHermitian connectionTangent spaceAffine connectionRigid transformationAffine spaceLinear mapHolomorphic vector bundleParallel transportGauge theoryLevi-civita connectionTangential and normal componentsMeasurable functionTranslation of axesEhresmann connectionTautological bundleSymmetric bilinear formEuclidean topologyDirac equation in curved spacetimeAffine transformationCanonical bundleEuclidean groupCurvature formMean curvatureLie bracket of vector fieldsBilinear mapParametrizationFirst fundamental formIsometry groupSpin connectionCalculus on euclidean spaceRiemannian geometryLinking numberCongruenceEuler classSymplectic manifoldTensor productDivergence theoremEuclidean vectorBilinear formPseudo-riemannian manifoldSimply connected spaceParallel projectionRicci calculusContinuous linear operatorSecond covariant derivativeContact geometryTopological propertyHopf fibrationAdjunction formulaMetrizable spaceMean curvature flowAlternating multilinear mapHurewicz theoremHomeomorphismOrthogonal groupDual spaceLinear formCross productEuler characteristicCurve-shortening flowSpectral graph theoryConformal gravityEuclidean plane isometryEuler's rotation theoremSkew gradientRotation of axesFiber bundleDifferential structureDual systemClosed graph theoremConnection formInvariantTopologyRiemann curvature tensorProduct topologyTopological graphInvariant subspaceAssociated bundleGeometric topologyMean value theoremTangential quadrilateralSectionLinear functionParallelizable manifoldLocal diffeomorphismCanonical mapHamiltonian vector fieldHyperbolaLie algebraExponential mapRiemannian manifoldEinstein tensorTangent vector