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 | References | Similar Articles | Additional Information

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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Additional Information

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