Histoire de la réductibilité du groupe conforme des variétés riemanniennes (1964-1994)

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1. [A1] D.V. ALEKSEEVSKII. - Groups of transformations of Riemannian spaces, Mat. Sbornik, 89 (131) ( 1972), n° 2 and Math. USSR Sbornik 18 (2) ( 1972), 285-301. Zbl0263.53029MR334077
2. [A2] D.V. ALEKSEEVSKII. - Sn et En sont les seuls espaces riemanniens admettant une transformation conforme essentielle, Uspehi Mat. Nauk 28 (5) ( 1973), 225-226 (en russe). Zbl0284.53035
3. [B] N. BOURBAKI. - Topologie générale, Ch. III, Hermann, Paris, 1960. Zbl0102.27104
4. [C-H] A. CALABI and P. HARTMAN. - On the smoothness of isometries, Duke Math. J. 37 (4) ( 1970), 741-750. Zbl0203.54304MR283727
5. [F 1] J. LELONG-FERRAND. - Transformations conformes et quasi-conformes des variétés riemanniennes compactes, Mém. Acad. Royale de Belgique, 39 (5) ( 1970), 1-44 ; résumé dans C. R. Acad. Sci. Paris Sér. I Math. 269 ( 1969). 583-586. Zbl0201.09701
6. [F 2] J. LELONG-FERRAND. - Invariants conformes globaux sur les variétés riemanniennes, J. of Diff. Geo., 8 ( 1973). 487-510 ; résumé dans C. R. Acad. Sci. Paris Sér. I Math. 275 ( 1972), 119-122. Zbl0241.53027MR346702
7. [F 3] J. LELONG-FERRAND. - Construction de modules de continuité dans le cas limite de Soboleffet applications à la géométrie différentielle, Arch. for Rat. Mech. and An., 52 (4) ( 1973), 297-311 ; résumé dans C. R. Acad. Sci. Paris Sér. I Math. 276 ( 1973). 297-300. Zbl0245.46041MR345039
8. [F 4] J. LELONG-FERRAND. - Geometrical interpretation of scalar curvature and regularity of conformal homeomorphisms. Differential geometry and relativity, D. Reidel, Dordrecht ( 1976), 91-105 ; résumé dans C.R. Acad. Sci. Paris Sér.I Math. 284 ( 1977), 77-79. Zbl0345.53028MR442846
9. [F 5] J. LELONG-FERRAND. - Regularity of conformal mappings of Riemannian manifolds, Proc. Romanian Finnish Seminar Bucharest 1976, Lecture Notes 743 ( 1979), Springer-Verlag, 197-203. Zbl0426.30018MR552882
10. [F 6] J. LELONG-FERRAND. - Sur un lemme d'Alekseevskii relatif aux transformations conformes, C. R. Acad. Sci. Paris Sér. I Math. 284 ( 1977). 121-123. Zbl0339.53028
11. [F 7] J. FERRAND. - Le groupe des automorphismes conformes d'une variété de Finsler compacte, C.R. Acad. Sci. Paris Sér.I Math. 291 ( 1980), 209-210. Zbl0451.53051MR594293
12. [F 8] J. FERRAND. - Les géodésiques des structures conformes, C.R. Acad. Sci. Paris Sér.I Math. 294 ( 1982), 629-632. Zbl0487.53011MR664297
13. [F 9] J. FERRAND. - Un invariant conforme lié aux géodésiques conformes, Lecture Notes 1013 Springer ( 1983), 76-86. Zbl0543.53011MR738083
14. [F 10] J. FERRAND. - The action of conformal transformations on a Riemannian manifold, Math. Ann., 304 ( 1996), 277-291 ; résumé dans C.R. Acad. Sci. Paris Sér.I Math. 218 ( 1994), 213-216. Zbl0866.53027MR1371767
15. [F 11] J. FERRAND. - Convergence and degeneracy of quasiconformal maps of Riemannian manifolds, J. Analyse Math., 69 ( 1996), 1-24 ; résumé dans C.R. Acad. Sci. Paris Sér.I Math. 319 ( 1994), 437-440. Zbl0871.53031MR1296768
16. [F 12] J. FERRAND. - Conformal capacities and conformally invariant functions on Riemannian manifolds, Geometriae dedicata, 61 ( 1996), 103-120; résumé dans C.R. Acad. Sci. Paris Sér.I Math. 318 ( 1994). 213-216. Zbl0858.53009MR1262898
17. [F 13] J. FERRAND. - Conformal capacities and extremal metrics, Pacific J. of Math. 180 (1) ( 1997), 41-49. Zbl0885.53042MR1474892
18. [F 14] J. FERRAND. - Generalized condensers and conformal properties of Riemannian manifolds with at least two ends, Séminaire de théorie spectrale et géométrie, Grenoble 17 ( 1999). Zbl0976.53040MR1752695
19. [F 15] J. FERRAND. - Conditions d'existence et propriétés d'une métrique conformément invariante sur les variétés riemanniennes non-compactes, Analysis and topology, World scientific Singapore ( 1998), (dedicated to the memory of R. Stoilow) 285-291. Zbl0951.53026MR1667816
20. [G] K.R. GUTSCHERA. - Invariant metrics for groups of conformal transformations, Preprint, 1994. 
21. [I-M] T. IWANIEC and G. MARTIN. - Quasiregular mappings in even dimensions, Acta Math. 170 ( 1992), 29-81. Zbl0785.30008MR1208562
22. [K-N] S. KOBAYASHI and K. NOMIZU. - Foundations of differential geometry, vol.I, Interscience publishers, 1963. Zbl0119.37502MR152974
23. [K] S. KOBAYASHI. - Transformation groups in differential geometry, Erg. der Math., 70, Springer, 1972. Zbl0246.53031MR355886
24. [Ku] N.H. KUIPER. - On conformally flat spaces in the large, Ann. of Math.50 ( 1949), 916-924. Zbl0041.09303MR31310
25. [L] J. LAFONTAINE. - The theorem of Lelong-Ferrand and Obata. Conformal geometry, R. Kulkarni and U. Pinkall, ed. Max Planck Inst. fur Math. Bonn, 1988. Zbl0668.53022MR979790
26. [Mo] G.D. MOSTOW. - Quasiconformal mappings in n-space and the rigidity of hyperbolic space forms, Inst. Hautes Études Sci. Publ. Math. 34 ( 1968), 53-104. Zbl0189.09402MR236383
27. [M-S] S. MYERS and N. STEENROD. - The group of isometries of a Riemannian manifold, Ann. of Math.40 ( 1939), 400-416. Zbl0021.06303MR1503467
28. [M-Z1] D. MONTGOMERY and L. ZIPPIN. - Existence of subgroups isometric to the real numbers, Ann. of Math.53 ( 1951), 298-326. Zbl0045.31202MR47668
29. [M-Z2] D. MONTGOMERY and L. ZIPPIN. - Topological transformation groups, Interscience publishers, New-York-London, 1955. Zbl0068.01904MR73104
30. [O1] M. OBATA. - Conformal transformations of Riemannian manifolds, J. Differential Geom. 4 ( 1970), 311-333. Zbl0205.52003MR267485
31. [O2] M. OBATA. - The conjectures on conformal transformations of Riemannian manifolds, J. Differen-tial Geom. 6 ( 1971), 247-258. Zbl0236.53042MR303464
32. [P] R.S. PALAIS. - On the differentiability of isometries, Proc. Amer. Math. Soc.8 ( 1957), 805-807. Zbl0084.37405MR88000
33. [R 1] M.S. RAGHUNATHAN. - Discrete subgroups of Lie groups, Springer-Verlag, Berlin, 1972. Zbl0254.22005MR507234
34. [R 2] Y.G. RESHETNYAK. - On conformal mappings of a space. Soviet. Math. Dokl.1 ( l960), 153-155. Zbl0099.37901MR119169
35. [R 3] Y.G. RESHETNYAK. - Differential properties of quasiconformal maps and conformal maps of Riemannian manifolds, Siber. Math.J.19 (5) ( 1978), 1166-1183. Zbl0395.30014MR508507
36. [S] S. STERNBERG. - Lectures on differential geometry, Prenctice Hall, Englewood Cliffs, New Jersey, 1964. Zbl0129.13102MR193578
37. [V] J. VÄISÄLÄ. - Lectures on n-dimensional quasiconformal mappings, Lecture Notes in Math., 229 Springer-Verlag, Berlin, 1971. Zbl0221.30031MR454009
38. [Y] Y. YOSHIMATSU. - On a theorem of Alekseevskii concerning conformal transformations, J. Math. Soc. Japan 28 (2) ( 1976), 278-289. Zbl0318.53043MR405286