1 / 20

Duality for Immersed Manifolds

Duality for Immersed Manifolds. Daniel Dreibelbis University of North Florida USA. Umbilic Bracelet. Outline. Define duals and dual generalizations. Describe the singularities of duals of hypersurfaces. Define dual sphere bundles, and connect their singularities.

step
Download Presentation

Duality for Immersed Manifolds

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Duality for Immersed Manifolds Daniel Dreibelbis University of North Florida USA

  2. Umbilic Bracelet

  3. Outline • Define duals and dual generalizations. • Describe the singularities of duals of hypersurfaces. • Define dual sphere bundles, and connect their singularities. • Specific examples: asymptotic and binormal vectors for immersed manifolds • Explicit examples for surfaces in 4-D and 3-manifolds in 6-D

  4. Dual Hypersurfaces

  5. Dual - Curves

  6. Dual - Surfaces

  7. Duals from Sphere Bundles

  8. Duals from Sphere Bundles

  9. Duals between Sphere Bundles

  10. Generalizing Duals

  11. Examples We Can See

  12. Curves in R4

  13. Dimension = Codimension

  14. Examples: Surfaces in R4 Asymptotic Directions vs. Binormal Directions at a point

  15. Examples: Surfaces in R4 Asymptotics Binormals

  16. Singularity Curves on the Surface

  17. Examples: 3-manifolds in R6 Asymptotic Directions vs. Binormal Directions at a point Away from inflection points, asymptotic vectors and binormal vectors are projectively equivalent.

  18. Examples: 3-manifolds in R6 At inflections, the curves may or may not be projectively equivalent.

  19. Singularity Sets on the 3-manifold

  20. Thanks! • www.unf.edu/~ddreibel

More Related