I could not find any information on who translated the book. However, it is given for the courageous reader!" At one point, Cartan describes a formula as " simple and easy (and important!) to remember" (italics his). At another, he says, "The remainder of the proof may be left aside by the reader who dislikes calculations. Readers familiar with Cartan's other books will recognize some "Cartanisms." I particularly like the notion of "primitive of a form/function along a path," later generalized to "primitive of a form/function along a homotopy"! (This is the first time I've seen an author worry about how many times a function needs to be differentiable for certain theorems to work!) It is all extremely well done. The treatment is almost always elegant and complete, with careful attention to the underlying assumptions, particularly with respect to differentiability. Even the typeface is reminiscent of Bourbaki, in fact.
Proofs are done in a take-no-prisoners style reminiscent of Bourbaki (no accident, of course). Exterior products are taken with respect to a chosen bilinear pairing. For example, whenever possible, he works in a general Banach space E rather than in the special case of R n. Indeed, the Cours de calcul différentiel (whose latest edition includes both parts) seems not to be available in French either, at least according to .Ĭartan's approach is fearlessly general. As far as I know, that volume has not been published in English. Material from the first part of Cartan's differential calculus text is assumed and often referred to. It includes a long chapter on, yes, differential forms, but there are also chapters on the calculus of variations and on differential geometry. Instead, it is a part of Cartan's course on differential calculus. The title suggests that this is a book about differential forms.
(1953) Zbl0053.This is a very good book indeed, but it is not quite the book I thought it was. Théorie des points proches sur les variétés différentiables, Colloque de Géometrie Différentielle, C.N.R.S.An introduction to the D-Modules, Bull.142, London Mathematical Society, Cambridge University Press, New York, 1989, pp. . The Geometry of Jet Bundles, Lecture Notes Series, vol.Prolongament formel des systemes differentiels exterieurs d’ordre superieur, C.Sobre los espacios de jets y los fundamentos de la teoría de los sistemas de ecuaciones en derivadas parciales, Ph.D.Geometry of jet bundles and the structure of Lagrangian and Hamiltonian formalism, Lect.Natural Operations in Differential Geometry, Springer-Verlag, Berlin, 1993, pp. .On the higher order Poincaré-Cartan forms, Czechoslovak Math. Symplectic connections in geometric quantization and factor orderings, Ph.D.An exterior differential system approach to the Cartan form, Géométrie Symplectique et Physique Mathématique (Boston), P.
Symposium on Modern Developments in Analytical Mechanics (Bologna), Tecnoprint, 1983, pp. 127–147.
0 kommentar(er)
