Simple tangential families and perestroikas of their envelopes

Details Simple tangential families and perestroikas of their envelopes Simple tangential families and perestroikas of their envelopes

2004-09-06

arxiv.org/abs/math/0409089v1

Mathematics

Differential Geometry

11 pages

Scientific paper

Tangential families are 1-parameter families of rays emanating tangentially from smooth curves. We classify tangential family germs up to Left-Right equivalence: we prove that there are two infinite series and four sporadic simple singularities of tangential family germs (in addition to two stable singularities). We give their normal forms and miniversal tangential deformations (i.e., deformations among tangential families), and we describe the corresponding envelope perestroikas of small codimension. We also discuss envelope singularities of non simple tangential families.

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