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Bitangencies on Higher Dimensional Immersed Manifolds

This resource by Daniel Dreibelbis explores bitangencies on immersed manifolds. It delves into the problem definition, transitions in bitangencies, second and third order geometry, tangent and non-tangent translations, and more. The material covers line, curve, and surface bitangencies, as well as asymptotic vectors, hyperbolic and elliptic points, and singularities at parabolic points. The text also discusses conjugate planes, signs of bitangencies, and final formulas related to these concepts.

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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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