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Geometric flowLaplace operatorExterior covariant derivativeLie bracket of vector fieldsDifferential formDivergenceRicci flowDivergence theoremFunctional derivativeDifferential invariantTensor calculusEinstein tensorGradientSecond covariant derivativeVector fieldMetric tensorLie theorySymplectic manifoldLiouville field theoryDarboux's theoremRicci calculusCalculus on euclidean spaceDifferential geometrySymplectic geometryRiemann curvature tensorRicci curvatureHessian matrixAffine connectionDifferentiable curveElectromagnetic tensorEuler's formulaLie algebra representationMatrix differential equationDirectional derivativeDirac equation in curved spacetimeSecond fundamental formFractal derivativeAdjoint representationPoisson manifoldGeneralizations of the derivativeLie algebraTensor fieldRiemannian geometryDifferential geometry of surfacesLegendre transformationCartan decompositionCurlLagrange's identityTime dependent vector fieldBilinear formScalar fieldPartial derivativeGauge covariant derivativeMean curvature flowMultivariable calculusDifferential topologyLinear differential equationStructure tensorDifferential equationOrdinary differential equationTopological vector spaceTensor algebraFormal derivativeAlgebraic analysisPartial differential equationSpin structureLinear formGauge theoryCoarea formulaSymplectic vector spaceCotangent bundleLaplace transformGraph fourier transformDifferential operatorIndefinite orthogonal groupLagrangian functionFunctional analysisGeneral covarianceCovariant derivativeConnectorFlow velocityBiharmonic equationBifurcation theoryDensity on a manifoldExterior derivativeLaplace expansionDifferentiable manifoldClass field theoryEuler's theoremDelay differential equationDyadicsGradient theoremPseudodifferential operatorCalculusGlobal analysisDifferential structureGeneralized stokes theoremTime-scale calculusSimons' formulaSchmidt decomposition