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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

Groups of diffeomorphisms and their subgroups


Author: Hideki Omori
Journal: Trans. Amer. Math. Soc. 179 (1973), 85-122
MSC: Primary 58D05
DOI: https://doi.org/10.1090/S0002-9947-1973-0377975-0
MathSciNet review: 0377975
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Abstract: This paper has two purposes. The first is to prove the existence of a normal coordinate with respect to a connection defined on the group of diffeomorphisms of a closed manifold, relating to an elliptic complex. The second is to prove a Frobenius theorem with respect to a right invariant distribution defined on the group of diffeomorphisms of a closed manifold, relating to an elliptic complex. Consequently, the group of all volume preserving diffeomorphisms and the group of all symplectic diffeomorphisms are Fréchet Lie groups.


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DOI: https://doi.org/10.1090/S0002-9947-1973-0377975-0
Keywords: ILH-Lie group (strong), Fréchet Lie group, Frobenius theorem, ILH-connection
Article copyright: © Copyright 1973 American Mathematical Society