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Recently I was reintroduced to these two notions through a colloquium lecture, where the speaker briefly explained the concepts. I knew about the envelope of a family of plane curves but never thought of its generalization for surfaces. Due to the beauty of this topic, I tried to study it more closely, but couldn't find a suitable source to do so. Every modern differential geometry book I have consulted has completely ignored these concepts. (I guess the reason is that they have no equivalents in abstract manifolds. Am I right?)

Can anyone direct me to a book or lecture notes or some other source that discusses these concepts in modern language?

Bumblebee
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  • Have you searched for envelopes here? To get you started, here and here are a few answers I've written. You might look at some books on singularity theory — rather than differential geometry — for discussion of cuspidal edges, swallowtails, etc. – Ted Shifrin Sep 20 '22 at 18:45
  • @TedShifrin: Thanks for the links. Do you know any introductory book to singularity theory that discusses the topic you mentioned? Also, would you like to write an answer to this question elaborating g your comment? – Bumblebee Sep 21 '22 at 04:27
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    I haven't looked at these books in years, but try Bruce & Giblin Curves and Singularities. – Ted Shifrin Sep 21 '22 at 04:42

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