Structures · Geometry
IsManifold
Typeclass defining manifolds with respect to a model with corners, over a
field 𝕜. This definition includes the model with corners I (which might allow boundary, corners,
or not, so this class covers both manifolds with boundary and manifolds without boundary), and
a smoothness parameter n : ℕ∞ω (where n = 0 means topological manifold, n = ∞ means
smooth manifold and n = ω means analytic manifold).
- Shape
- 3 explicit arguments
Extends1
Extended by2
Concrete types that are instances2
- Real
- Complex
How is a type an instance?
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Assumed by348
- tangentBundleCore
- IsManifold.chart_mem_maximalAtlas
- tangentCoordChange
- inTangentCoordinates
- SmoothBumpCovering.toSmoothPartitionOfUnity
- tangentBundleCore_coordChange
- SmoothBumpCovering.toBumpCovering
- mdifferentiableWithinAt_extChartAt_symm
- IsManifold.subset_maximalAtlas
- UniqueMDiffOn.uniqueDiffOn_target_inter
- mdifferentiableAt_extChartAt
- tangentBundleCore_indexAt
- CovariantDerivative.torsion
- IsManifold.of_le
- IsCovariantDerivativeOn.torsion
- ContMDiffWithinAt.mpullbackWithin_vectorField_inter
- contMDiffWithinAt_iff_of_mem_source
- contMDiff_iff
- ContMDiffWithinAt.mpullback_vectorField_preimage
- mfderivWithin_extChartAt_symm_comp_mfderiv_extChartAt'
- MDifferentiableWithinAt.differentiableWithinAt_mpullbackWithin_vectorField
- ae_eq_zero_of_integral_contMDiff_smul_eq_zero
- mfderivWithin_extChartAt_symm_comp_mfderiv_extChartAt
- hasMFDerivWithinAt_extChartAt
- mdifferentiableAt_atlas
- VectorField.contMDiffWithinAt_mpullbackWithin_extChartAt_symm
- hasMFDerivAt_extChartAt
- VectorField.mlieBracketWithin_smul_right
- ContMDiffWithinAt.mfderivWithin_const
- UniqueMDiffOn.uniqueMDiffOn_target_inter
- ContMDiffWithinAt.mpullbackWithin_vectorField_of_mem
- contMDiffWithinAt_iff_contMDiffOn_nhds
- ContMDiffWithinAt.mfderivWithin
- MDifferentiableWithinAt.mpullback_vectorField_preimage
- mfderiv_extChartAt_comp_mfderivWithin_extChartAt_symm
- SmoothPartitionOfUnity.exists_isSubordinate
- contMDiffWithinAt_iff_contMDiffWithinAt_nhdsWithin
- ContMDiffWithinAt.mlieBracketWithin_vectorField
- mdifferentiableWithinAt_iff_of_mem_source
- contMDiffAt_extChartAt'
- mdifferentiableAt_atlas_symm
- isInvertible_mfderivWithin_extChartAt_symm
- ContMDiff.contMDiff_tangentMap
- VectorField.mpullback_mlieBracketWithin
- MDifferentiableWithinAt.mpullbackWithin_vectorField_inter
- exists_contMDiffMap_zero_one_of_isClosed
- VectorField.mpullback_mlieBracket
- VectorField.mpullbackWithin_mlieBracketWithin'
- VectorField.eventuallyEq_mpullback_mpullbackWithin_extChartAt
- TangentBundle.continuousLinearMapAt_trivializationAt_eq_core