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- Affine_focal_set abstract "In mathematics, and especially affine differential geometry, the affine focal set of a smooth submanifold M embedded in a smooth manifold N is the caustic generated by the affine normal lines. It can be realised as the bifurcation set of a certain family of functions. The bifurcation set is the set of parameter values of the family which yield functions with degenerate singularities. This is not the same as the bifurcation diagram in dynamical systems.Let us assume that M is an n-dimensional smooth hypersurface in real (n+1)-space. We assume that M has no points where the second fundamental form is degenerate. We recall from the article affine differential geometry that there is a unique transverse vector field over M. This is the affine normal vector field, or the Blaschke normal field. A special (i.e. det = 1) affine transformation of real (n + 1)-space will carry the affine normal vector field of M onto the affine normal vector field of the image of M under the transformation.".
- Affine_focal_set wikiPageID "18906055".
- Affine_focal_set wikiPageLength "11678".
- Affine_focal_set wikiPageOutDegree "74".
- Affine_focal_set wikiPageRevisionID "663894154".
- Affine_focal_set wikiPageWikiLink Affine_connection.
- Affine_focal_set wikiPageWikiLink Affine_differential_geometry.
- Affine_focal_set wikiPageWikiLink Affine_transformation.
- Affine_focal_set wikiPageWikiLink Bifurcation_diagram.
- Affine_focal_set wikiPageWikiLink Blaschke_normal_field.
- Affine_focal_set wikiPageWikiLink Catastrophe_theory.
- Affine_focal_set wikiPageWikiLink Category:Differential_geometry.
- Affine_focal_set wikiPageWikiLink Caustic_(mathematics).
- Affine_focal_set wikiPageWikiLink Chord_(geometry).
- Affine_focal_set wikiPageWikiLink Covariant_derivative.
- Affine_focal_set wikiPageWikiLink Cusp_(singularity).
- Affine_focal_set wikiPageWikiLink Degenerate_bilinear_form.
- Affine_focal_set wikiPageWikiLink Determinant.
- Affine_focal_set wikiPageWikiLink Diagonalizable_matrix.
- Affine_focal_set wikiPageWikiLink Diffeomorphism.
- Affine_focal_set wikiPageWikiLink Differentiable_manifold.
- Affine_focal_set wikiPageWikiLink Differential_form.
- Affine_focal_set wikiPageWikiLink Dimension.
- Affine_focal_set wikiPageWikiLink Dynamical_system.
- Affine_focal_set wikiPageWikiLink Eigenvalues_and_eigenvectors.
- Affine_focal_set wikiPageWikiLink Embedding.
- Affine_focal_set wikiPageWikiLink Floor_and_ceiling_functions.
- Affine_focal_set wikiPageWikiLink Function_(mathematics).
- Affine_focal_set wikiPageWikiLink Generic_property.
- Affine_focal_set wikiPageWikiLink Geometry.
- Affine_focal_set wikiPageWikiLink Hessian_matrix.
- Affine_focal_set wikiPageWikiLink Hypersurface.
- Affine_focal_set wikiPageWikiLink Identity_element.
- Affine_focal_set wikiPageWikiLink Infinitesimal.
- Affine_focal_set wikiPageWikiLink Jacobian_matrix_and_determinant.
- Affine_focal_set wikiPageWikiLink Line–line_intersection.
- Affine_focal_set wikiPageWikiLink Local_property.
- Affine_focal_set wikiPageWikiLink Manifold.
- Affine_focal_set wikiPageWikiLink Modulus_of_continuity.
- Affine_focal_set wikiPageWikiLink Negative_number.
- Affine_focal_set wikiPageWikiLink Neighbourhood.
- Affine_focal_set wikiPageWikiLink Net_(polyhedron).
- Affine_focal_set wikiPageWikiLink Open_set.
- Affine_focal_set wikiPageWikiLink Parallel_(geometry).
- Affine_focal_set wikiPageWikiLink Parametrization.
- Affine_focal_set wikiPageWikiLink Partial_derivative.
- Affine_focal_set wikiPageWikiLink Plane_curve.
- Affine_focal_set wikiPageWikiLink Power_series.
- Affine_focal_set wikiPageWikiLink Principal_curvature.
- Affine_focal_set wikiPageWikiLink Riemann_curvature_tensor.
- Affine_focal_set wikiPageWikiLink Second_fundamental_form.
- Affine_focal_set wikiPageWikiLink Sign_(mathematics).
- Affine_focal_set wikiPageWikiLink Singularity_(mathematics).
- Affine_focal_set wikiPageWikiLink Singularity_theory.
- Affine_focal_set wikiPageWikiLink Solution.
- Affine_focal_set wikiPageWikiLink Submanifold.
- Affine_focal_set wikiPageWikiLink Tangent.
- Affine_focal_set wikiPageWikiLink Tangent_space.
- Affine_focal_set wikiPageWikiLink Tensor_field.
- Affine_focal_set wikiPageWikiLink Torsion_tensor.
- Affine_focal_set wikiPageWikiLink Transversality_(mathematics).
- Affine_focal_set wikiPageWikiLink Vector_field.
- Affine_focal_set wikiPageWikiLink Vladimir_Arnold.
- Affine_focal_set wikiPageUsesTemplate Template:Inappropriate_person.
- Affine_focal_set wikiPageUsesTemplate Template:Multiple_issues.
- Affine_focal_set wikiPageUsesTemplate Template:Orphan.
- Affine_focal_set subject Category:Differential_geometry.
- Affine_focal_set type Physic.
- Affine_focal_set comment "In mathematics, and especially affine differential geometry, the affine focal set of a smooth submanifold M embedded in a smooth manifold N is the caustic generated by the affine normal lines. It can be realised as the bifurcation set of a certain family of functions. The bifurcation set is the set of parameter values of the family which yield functions with degenerate singularities.".
- Affine_focal_set label "Affine focal set".
- Affine_focal_set sameAs Q4688940.
- Affine_focal_set sameAs m.04jfzk7.
- Affine_focal_set sameAs Q4688940.
- Affine_focal_set wasDerivedFrom Affine_focal_set?oldid=663894154.
- Affine_focal_set isPrimaryTopicOf Affine_focal_set.