Non-English-language graduate-level textbooks on differential geometry

Question

I'm looking for modern graduate-level non-English-language differential geometry textbooks. I'm interested in original works by non-English-language speakers in their native languages, not translations into non-English languages. I'm also not interested in non-English language textbooks which are available in English translations, such as Manfredo Perdigão do Carmo's "Riemannian geometry".

I have already made a list of about 45 English-language textbooks, and I have already acquired the following non-English-language DG books.

Francisco Gómez Ruiz, "Geometría diferencial y geometría de Riemann", 2015.
Rolf Sulanke, Peter Wintgen, "Differentialgeometrie und Faserbündel", 1972.
Paul Malliavin, "Géométrie différentielle intrinsèque", 1972.
Yvonne Choquet-Bruhat, "Géométrie différentielle et systèmes extérieurs", 1968.

Most of these are not recent. On the standard online bookshop web sites, I have only found elementary books on classical non-intrinsic differential geometry in non-English languages. I'm really looking for up-to-date graduate-level books like the Gomez Ruiz book. And by the way, not in CJK languages please. I can struggle through most languages with a dictionary, but Chinese characters are just a bit too much work for me.

My purpose is to include the books in the bibliography of a book I'm writing. I would also like to read them myself!

score 2 · Answer 1 · answered Jun 17 '15 at 12:42

2

Time ago a read a really nice book "Geometria de espacios fibrados" (Spanish) writen by Roberto J. Miatello and Carlos E. Olmos in 1992 and published in Serie "B" Trabajos de Matematica, FaMAF, Universidad Nacional de Cordoba, Argentina. Prof. Olmos is well known expert in Riemannian Geometry that in 2005 gave a geometric proof of a famous theorem by Marcel Berger : http://annals.math.princeton.edu/wp-content/uploads/annals-v161-n1-p11.pdf

answered Jun 17 '15 at 12:42

Holonomia

2,543

Thanks. I've found it listed here: http://www2.famaf.unc.edu.ar/publicaciones/publicaciones.html, with the date 1990. It seems to indicate a PDF download link, but there's no link. And it doesn't show up in google for any online bookshops. I'll keep trying though. – Alan U. Kennington Jun 17 '15 at 12:57
Yes, there the date is 1990 and indeed there's no link. The 1992 one is a second edition. Looking at internet I find Olmos' email : [email protected] I think he can send to you a pdf file of this book. – Holonomia Jun 17 '15 at 15:42
Well, I hope he won't mind. I'll try it. If the book is good, it should be re-published, or at least it should put on the web for download. Muchas gracias de nuevo. – Alan U. Kennington Jun 17 '15 at 17:09

score 2 · Answer 2 · edited Apr 13 '17 at 12:19

Lafontaine: Introduction aux variétés différentielles
A rigorous, classical treatise. The second edition is much more complete.

Bröcker-Jänich: Einführung in Die Differentialtopologie
A remarkable booklet which goes very far in few pages. Many beautiful illustrations.

Pham: Géométrie et calcul différentiel sur les variétés
A very original book, explaining the intuition behind the concepts and written by a physicist turned mathematician, whom I had the good luck to have as a colleague.

Berger-Gostiaux: Géométrie différentielle
A beautiful blend of modern and classical topics. This is the only book I know which computes in extreme detail the volume of tubes (a calculation due to Hotelling and Weyl).
A fly in the ointment is the pedantic precision in the notation: some abuse of notation would have made for smoother reading!

Laudenbach: Transversalité, courants et théorie de Morse
A very advanced book, involving Reeb foliations, De Rham currents, Thom-Smale- Witten complexes,...

Dieudonné: Eléments d'analyse; Tomes III,IV,IX
Wikipedia describes in detail the contents of the nine (!) tomes of Dieudonné's encyclopaedic treatise, of which at least the tomes III,IV,IX are relevant to the question.
What he wrote on his own (a truly superhuman accomplishment!) can be seen as advantageously replacing the treatise on analysis that Bourbaki originally set out to provide but never did.

Edit:
Bernhard Riemann: Über die Hypothesen, Welche der Geometrie zu Grunde Liegen
Riemann's foundational text in all its glory, with accompanying articles by modern historians and scientists.

Bitte sehr et bonne lecture, dear Alan ! (I have added a reference containing Riemann's inaugural dissertation and various related articles) — Georges Elencwajg, Jun 17 '15 at 16:40
Yes, thanks. I have the original edition with commentary by Weyl. But the one you refer to is much more modern, with additional commentary by Jürgen Jost. It isn't a graduate-level textbook, but I will buy one anyway because Riemann's original thesis was difficult to understand. Noch mal vielen Dank et merci. — Alan U. Kennington, Jun 17 '15 at 16:55

score 0 · Answer 3 · answered Aug 27 '19 at 23:52

0

Brazilian books.

www. im.ufal.br > posmat > index.php > downloads > category > 6-livros

www.sbm.org.br > wp-content > uploads > 2016/06 > Introdução-a-Geometria-Diferencial

answered Aug 27 '19 at 23:52

Marta Oliveira

49

Non-English-language graduate-level textbooks on differential geometry

3 Answers3