Bitangencies on Higher Dimensional Immersed Manifolds Daniel Dreibelbis University of North Florida USA ddreibel.

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