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Basic aspects of differential geometry

Abstract : This is a very partial description of differential geometry as elaborated by Élie Cartan and expressed in a suitable language by Charles Ehresmann. I am entirely responsable for the selection of materials and for the mistakes, if any. The framework is that of smooth (finite dimensional) manifolds and maps, whose definition is taken for granted-most of the notions we consider "pass" without any problem to the real analytic and (replacing R by C) complex and/or Banach categories. The k th derivative of a map f is denoted by D^k f as in [10]. Paths are defined on intervals.
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https://hal-univ-paris.archives-ouvertes.fr/hal-03838511
Contributor : Marc Chaperon Connect in order to contact the contributor
Submitted on : Thursday, November 3, 2022 - 3:47:35 PM
Last modification on : Thursday, November 10, 2022 - 4:30:10 AM

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2019 Ehresmann.pdf
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Marc Chaperon. Basic aspects of differential geometry. Geometry in History, Springer, 2019, ⟨10.1007/978-3-030-13609-3_15⟩. ⟨hal-03838511⟩

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