The Geometry of Flecnodal Pairs
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We generalize the definition of a flecnode on a surface in ℝ3 to a definition for a general immersed manifold in Euclidean space. Instead of considering a flecnode as a point on the manifold, we consider it as a pair of a normal vector and a tangent vector, called the flecnodal pair. The structure of this set is considered, as well as its connection to binormals and A 3 singularities in the set of height functions. The specific case of a surface immersed in ℝ4 is studied in more detail, with the generic singularities of the flecnodal normals and the flecnodal tangents classified. Finally, the connection between the flecnodals and bitangencies are studied, especially in the case where the dimension of the manifold equals the codimension.
KeywordsFlecnode differential geometry
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