I am looking especially for one particular work that deals with group theory and differential geometry.
"La Théorie des Groupes Finis et Continus et la Géométrie Différentielle traitées par la
Méthode du Repère Mobile" by Élie Cartan.
I'm afraid that there is no translation of this book - I own an old copy of it, it's not one of Cartan's strongest pieces of work. I've been reading in Cartan's complete works for many years, there are virtually no translations (at least, I never heard of any) and his style is really hard to understand, even if you know French perfectly. Sorry for the bad news.
oops that's indeed not so good news.... But you say it's not so strong a work of his... Can u throw some more light on the matter if I were to tell you where I need this work? Just started on "evolution of projective curves" for an application in computer vision and projective geometry. Any idea of some related contemporary works ?
I'm afraid no. This is by now such a large area, with many different approaches to the topic... but I think that Cartan is too old to be a good source for recent developments on this.
I have a partial "translation" that I have produced for my own benefit - I say "translation" because I have not checked it sufficiently carefully to be sure that there are no errors of translation. But, on the whole, it represents the content of the translated chapters sufficiently well.
I am not sure when I will have the time to complete it. I find the book interesting from an historical perspective. Essentially, Cartan invents the concept of a principal bundle in this and similar works, even though he does not explicitly formalise it. The "moving frame" is probably better translated as "the method of the local frame" but, history being what it is, this more apt name will probably never catch on.
Hi Fabio, that would be great. I have looked at a lot of places , but got nothing. If you don't mind sharing your translations I would really obliged. It would help me a lot. I found the treatment of moving frame methods for computer vision highly interesting. And after a hiatus I am back as a doctoral student . Hence your response couldn't have come at a more apt time.
My apologies, Snehal, I have only just seen your response. If you send me an email at [email protected], I will forward what I have by way of translation.
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