Groups of diffeomorphisms and their subgroups
HTML articles powered by AMS MathViewer
- by Hideki Omori PDF
- Trans. Amer. Math. Soc. 179 (1973), 85-122 Request permission
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.References
- J. Dieudonné, Foundations of modern analysis, Pure and Applied Mathematics, Vol. X, Academic Press, New York-London, 1960. MR 0120319
- David G. Ebin and Jerrold Marsden, Groups of diffeomorphisms and the motion of an incompressible fluid, Ann. of Math. (2) 92 (1970), 102–163. MR 271984, DOI 10.2307/1970699
- Serge Lang, Introduction to differentiable manifolds, Interscience Publishers (a division of John Wiley & Sons, Inc.), New York-London, 1962. MR 0155257
- J. A. Leslie, On a differential structure for the group of diffeomorphisms, Topology 6 (1967), 263–271. MR 210147, DOI 10.1016/0040-9383(67)90038-9
- J. A. Leslie, Some Frobenius theorems in global analysis, J. Differential Geometry 2 (1968), 279–297. MR 251750, DOI 10.4310/jdg/1214428441
- Hideki Omori, Homomorphic images of Lie groups, J. Math. Soc. Japan 18 (1966), 97–117. MR 188343, DOI 10.2969/jmsj/01810097
- Hideki Omori, On the group of diffeomorphisms on a compact manifold, Global Analysis (Proc. Sympos. Pure Math., Vol. XV, Berkeley, Calif., 1968) Amer. Math. Soc., Providence, R.I., 1970, pp. 167–183. MR 0271983
- Hideki Omori, Regularity of connections, Differential geometry (in honor of Kentaro Yano), Kinokuniya, Tokyo, 1972, pp. 385–399. MR 0388444
- Hideki Omori, Local structures of groups of diffeomorphisms, J. Math. Soc. Japan 24 (1972), 60–88. MR 295386, DOI 10.2969/jmsj/02410060
- Hideki Omori, On smooth extension theorems, J. Math. Soc. Japan 24 (1972), 405–432. MR 305441, DOI 10.2969/jmsj/02430405
- Sigeru Mizohata, Henbidun hôteisiki ron, Contemporary Mathematics, vol. 9, Iwanami Shoten, Tokyo, 1965 (Japanese). MR 0232070
- Deane Montgomery and Leo Zippin, Topological transformation groups, Interscience Publishers, New York-London, 1955. MR 0073104
- Katsumi Nomizu, Lie groups and differential geometry, Mathematical Society of Japan, Tokyo, 1956. MR 0084166
- Richard S. Palais, Seminar on the Atiyah-Singer index theorem, Annals of Mathematics Studies, No. 57, Princeton University Press, Princeton, N.J., 1965. With contributions by M. F. Atiyah, A. Borel, E. E. Floyd, R. T. Seeley, W. Shih and R. Solovay. MR 0198494, DOI 10.1515/9781400882045
- Lars Hörmander, On interior regularity of the solutions of partial differential equations, Comm. Pure Appl. Math. 11 (1958), 197–218. MR 106330, DOI 10.1002/cpa.3160110205
Additional Information
- © Copyright 1973 American Mathematical Society
- 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