Isometric Euclidean embeddings of a compact manifold from a Fréchet manifold

Binz, Ernst

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URN: urn:nbn:de:bsz:180-madoc-19594
Document Type: Working paper
Year of publication: 1987
The title of a journal, publication series: None
Publication language: English
Institution: School of Business Informatics and Mathematics > Sonstige - Fakultät für Wirtschaftsinformatik und Wirtschaftsmathematik
MADOC publication series: Veröffentlichungen der Fakultät für Mathematik und Informatik > Institut für Mathematik > Mannheimer Manuskripte
Subject: 510 Mathematics
Classification: MSC: 58D15 58B20 ,
Subject headings (SWD): Kompakte Einbettung , Einbettung <Mathematik> , Fréchet-Mannigfaltigkeit
Keywords (English): smooth embeddings , compact smooth manifold , Fréchet manifold
Abstract: Let E (M, IRn) be the collection of all smooth embeddings of a compact smooth manifold M into IRn. Given a fixed scalar product < , > on IRn , the pull-back of < , > by j &#8712; E(M , IRn) is denoted by m(j). We show that m-1(m(j)) is a Fréchet manifold for any j &#8712; E(M , IRn). This manifold is infinit dimensional if the codimension of M in IRn is large enough. The result links with Einstein's evolution equation and with elasticity theory.
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