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Self-Conjugate Vectors of Immersed Manifolds in R 6

Self-Conjugate Vectors of Immersed Manifolds in R 6. Daniel Dreibelbis University of North Florida USA. Shameless Self-promotion. www.unf.edu/~ddreibel/research. Outline. Define conjugate and self-conjugate vectors, focusing on the case of 3-manifolds in Euclidean 6-space.

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Self-Conjugate Vectors of Immersed Manifolds in R 6

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  1. Self-Conjugate Vectors of Immersed Manifolds in R6 Daniel Dreibelbis University of North Florida USA

  2. Shameless Self-promotion • www.unf.edu/~ddreibel/research

  3. Outline • Define conjugate and self-conjugate vectors, focusing on the case of 3-manifolds in Euclidean 6-space. • Look at connection between conjugate vectors and elliptic curves. • Classify generic structure of the parabolic set. • Classify generic transitions in a 1-parameter family of parabolic sets.

  4. Conjugate Vectors

  5. Special Case

  6. Description of Conjugate Vectors

  7. Curvature Veronese Surface

  8. Possible Configurations

  9. Elliptic Curves - Addition

  10. Conjugate Map • The conjugate map is the sum of an order 2 point:

  11. Almost Normal Form

  12. Classification • Same curve can have different conjugate maps, one for each point of order 2. • j-invariant and conjugate map determines affine type of conjugate curve

  13. Self-Conjugate Vectors

  14. Page 1

  15. Page 167

  16. Parabolic Set

  17. Generic Structure of the Parabolic Set

  18. Around a Triple Point

  19. Through a Pinch Point

  20. Generic Changes

  21. A3 vectors and Morse Transitions

  22. A3 vectors and Morse Transitions

  23. Quadruple Point

  24. Pinch Point Intersection

  25. Thanks! • www.unf.edu/~ddreibel/research

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