Equiaffine Darboux frames for codimension 2 submanifolds contained in hypersurfaces

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<p>Consider a codimension 1 submanifold Nn ⊂ Mn+1, where Mn+1 ⊂ ℝn+2 is a hypersurface. The envelope of tangent spaces of M along N generalizes the concept of tangent developable surface of a surface along a curve. In this paper, we study the singularities of these envelopes. </p><p>There are some important examples of submanifolds that admit a vector field tangent to M and transversal to N whose derivative in any direction of N is contained in N. When this is the case, one can construct transversal plane bundles and affine metrics on N with the desirable properties of being equiaffine and apolar. Moreover, this transversal bundle coincides with the classical notion of Transon plane. But we also give an explicit example of a submanifold that does not admit a vector field with the above property.</p>

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