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Generalized C n ‐Manifolds
Author(s) -
Gähler W.,
Firmanty M.
Publication year - 1983
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.19831130126
Subject(s) - differentiable function , characterization (materials science) , mathematics , manifold (fluid mechanics) , generalization , pure mathematics , differential topology , ricci flat manifold , topology (electrical circuits) , mathematical analysis , combinatorics , geometry , curvature , physics , mechanical engineering , scalar curvature , optics , engineering
This paper proves an important topological characterization of C MB n ‐manifolds and especially of arbitrary finite dimensional C n ‐manifolds and arbitrary C ∞‐BANACH manifolds. Whereas differentiability structures in the usual sense may be proper classes this characterization always enables a definition of differentiability structures as sets. Further this characterization suggests a suitable generalization of the notion of differentiable manifold which we call C n ‐manifold. C n ‐manifolds have a lot of better properties than C n ‐manifolds and may be useful therefore in physics and technics. Some examples of C n ‐manifolds are given in the last two sections defined by means of certain geometric structures.