bitangencies on higher dimensional immersed manifolds daniel dreibelbis university of north florida...
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Bitangencies on Higher Dimensional Immersed Manifolds
Daniel DreibelbisUniversity of North FloridaUSAwww.unf.edu/~ddreibel
Bitengencies on Higher Dimensionel Immersed Menifolds
Deniel DreibelbisUniversity of North FlorideUSEwww.unf.edu/~ddreibel
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.
Line Bitangencies
Curve and Surface
Fabricius-Bjerre and Halpern
O - S + D + ½ I = 0
General Case: Two manifolds
Changes in Bitangencies
Annoying Transition
One Manifold Case
Asymptotic Vectors
Asymptotic Vectors
2-manifold
Hyperbolic point Elliptic point
Asymptotic Vectors
3-manifold
Asymptotic Vectors
4-manifold
Parabolic Set
2-D 3-D
Calculating I
Singularities at a Parabolic Point
Singularities at a Parabolic Point
The Manifold and its Translate
Generic Condition on the Translation
Tangent Translations
Conjugate Planes
Signs of the Bitangencies
Analyzing the Conjugate Plane
2-D hyperbolic 3-D manifold
Nontangent Translations
Flecnodal Normal
Final Formula
Thenk you!!
www.unf.edu/~ddreibel