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On Lie algebras of vector fields with invariant submanifolds

Published online by Cambridge University Press:  22 January 2016

Akira Koriyama
Akira Koriyama*
Affiliation:
Department of Mathematics, Tokyo Metropolitan University and Department of Mathematics, Tokai University
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It is known (Pursell and Shanks [9]) that an isomorphism between Lie algebras of infinitesimal automorphisms of C∞ structures with compact support on manifolds M and M′ yields an isomorphism between C∞ structures of M and M’.

Omori [5] proved that this is still true for some other structures on manifolds. More precisely, let M and M′ be Hausdorff and finite dimensional manifolds without boundary. Let α be one of the following structures:

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 55 , November 1974 , pp. 91 - 110
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1974

References

[1] Bishop, L. and Goldberg, S., Tensor Analysis on Manifolds, The Macmillan Company, New York, 1968.Google Scholar
[2] Ebin, D. G. and Marsden, J., Groups of diffeomorphisms and motion of an incompressible fluid. Ann. Math., 92 (1970) 102–163.CrossRefGoogle Scholar
[3] Matushima, Y., Theory of Lie algebras (in Japanese), Kyoritu Shuppan.Google Scholar
[4] Nelson, E., TOPICS IN DYNAMICS I: FLOWS, Math. Notes, Princeton Univ. Press.Google Scholar
[5] Omori, H., On Lie algebras of vector fields, to appear.Google Scholar
[6] Omori, H., On groups of diifeomorphisms on a compact manifold, Proc. Symp. Pure Math. A.M.S. 15 (1970) 168–183.Google Scholar
[7] Omori, H., Groups of diffeomorphisms and their subgroups, to appear in Trans. A.M.S.Google Scholar
[8] Omori, H., On infinite dimensional Lie transformation groups, to appear.Google Scholar
[9] Pursell, L. E. and Shanks, , The Lie algebra of a smooth manifold, Proc. Amer. Math. Soc, (1954) 468–472.Google Scholar