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Bitangencies on Higher Dimensional Immersed Manifolds

Bitangencies on Higher Dimensional Immersed Manifolds. Daniel Dreibelbis University of North Florida USA www.unf.edu/~ddreibel. Bitengencies on Higher Dimensionel Immersed Menifolds. Deniel Dreibelbis University of North Floride USE www.unf.edu/~ddreibel. Outline. Define the problem.

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Bitangencies on Higher Dimensional Immersed Manifolds

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  1. Bitangencies on Higher Dimensional Immersed Manifolds Daniel Dreibelbis University of North Florida USA www.unf.edu/~ddreibel

  2. Bitengencies on Higher Dimensionel Immersed Menifolds Deniel Dreibelbis University of North Floride USE www.unf.edu/~ddreibel

  3. Outline Define the problem. Two manifold case. Transitions in bitangencies. One manifold case. Second and third order geometry. Tangent translations. Non-tangent translations. Putting it all together.

  4. Line Bitangencies

  5. Curve and Surface O - S + D + ½ I = 0 Fabricius-Bjerre and Halpern

  6. General Case: Two manifolds

  7. Changes in Bitangencies

  8. Annoying Transition

  9. One Manifold Case

  10. Asymptotic Vectors

  11. Asymptotic Vectors Hyperbolic point Elliptic point 2-manifold

  12. Asymptotic Vectors 3-manifold

  13. Asymptotic Vectors 4-manifold

  14. Parabolic Set 2-D 3-D

  15. Calculating I

  16. Singularities at a Parabolic Point

  17. Singularities at a Parabolic Point

  18. The Manifold and its Translate

  19. Generic Condition on the Translation

  20. Tangent Translations

  21. Conjugate Planes

  22. Signs of the Bitangencies

  23. Analyzing the Conjugate Plane 2-D hyperbolic 3-D manifold

  24. Nontangent Translations

  25. Flecnodal Normal

  26. Final Formula

  27. Thenk you!! • www.unf.edu/~ddreibel

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