The conjectures on conformal transformations of Riemannian manifolds

Journal of Differential Geometry

Volumn 6, Issue 2, 1971, Pages 247-258

  Obata, Morio ^a,b  

^a TOKYO METROPOLITAN UNIVERSITY   (Japan)

^b DURHAM UNIVERSITY   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 84972541914     PISSN: 0022040X     EISSN: 1945743X     Source Type: Journal    
DOI: 10.4310/jdg/1214430407     Document Type: Article

References (37)

1. A. Avez, Transformations conformes des variétés riemanniennes compactes, C. R. Acad. Sci. Paris 259 (1964) 4469-4472; 260 (1965) 1550-1553.
2. B. Ba, Structure presque complexe, structure conforme et derivations, Cahiers de Topologi. e et Géométrie Différentielle, C. N. R. S. Paris 8 (1966).
3. yune variété riemannienne compacte, C. R. Acad. Sci. Paris 260 (1965) 1547-1549.
4. R. L. Bishop & S. I. Goldberg, A characterization of the Euclidean sphere, Bull. Amer. Math. Soc. 72 (1966) 122-124.
5. E. Cartan, Les espaces à connexion conforme, Ann. Soc. Polon. Math. 2 (1923) 171-221.
6. S. I. Goldberg & S. Kabayashi, The conformal transformation group of a compact homogeneous manifold, Bull. Amer. Math. Soc. 68 (1962) 378-381.
7. S. I. Goldberg & S. Kabayashi, The conformal transformation group of a compact Riemannian manifold, Amer. J. Math. 84 (1962) 170-174.
8. V. Hlavatý, Zur Konformgeometrie, Proc. Acad. Amsterdam 38 (1935) 281-286.
9. C. C. Hsiung, On the group of conformal transformations of a compact Riemannian manifold. I, II, III, Proc. Nat. Acad. Sci. U. S. A. 54 (1965) 1509-1513; Duke Math. J. 34 (1967) 337-341; J. Differential Geometry 2 (1968) 185-190.
10. S. Ishihara, Groups of projective transformations and groups of conformal trans formations, J. Math. Soc. Japan 9 (1957) 195-227.
11. S. Ishihara & Y. Tashiro, On Riemannian manifolds admitting a concircular trans formation, Math. J. Okayama Univ. 9 (1959) 19-47.
12. S. Kabayashi, Le groupe de transformations qui laissent invariant un parallélisme, Colloque de Topologie, Ehresmann, Strasbourge, 1954.
13. S. Kabayashi, Theory of connections, Ann. Mat. Pura Appl. 43 (1957) 119-194.
14. N. H. Kuiper, On conformally-flat spaces in the large, Ann. of Math. 50 (1949) 916-924.
15. M. Kurita, A note on conformal mappings of certain Riemannian manifolds, Nagoya Math. J. 21 (1962) 111-114.
16. A. J. Ledger & M. Obata, Compact riemannian manifolds with essential groups of conformorphisms, Trans. Amer. Math. Soc. 150 (1970) 645-651.
17. J. Lelong-Ferrand, Transformations conformes et quasiconformes des variétés riemanniennes; application à la demonstration d'une conjeceure de A. Lichnero- wicz, C. R. Acad. Sci. Paris 269 (1969) 583-586.
18. A. Lichnerowicz, Géométrie des groupes de transformations, Paris, 1958.
19. A. Lichnerowicz, Sur les transformations conformes d'une variété riemannienne compacte, C. R. Acad. Sci. Paris 259 (1964) 697-700.
20. D. Montgomery & L. Zippin, Existence of subgroups isomorphic to the real num bers, Ann. of Math. 53 (1951) 298-326.
21. T. Nagano, On conformal transformations of Riemannian spaces, J. Math. Soc. Japan 10 (1958) 79-93.
22. T. Nagano, The conformal transformations on a space with parallel Ricci curvature, J. Math. Soc. Japan 11 (1959) 10-14.
23. M. Obata, Conformal transformations of compact Riemannian manifolds, Illinois J. Math. 6 (1962) 292-295.
24. M. Obata, Certain conditions for a Riemannian manifold to be isometric with a sphere, J. Math. Soc. Japan 14 (1962) 333-340.
25. M. Obata, Riemannian manifolds admitting a solution of a certain system of differential equations, Proc. U. S. -Japan Sem. Differential Geometry, Kyoto, Japan, 1965, 101-114.
26. M. Obata, Conformal transformations of Riemannian manifolds, J. Differential Ge ometry 4 (1970) 311-333.
27. M. Obata, Conformally fiat Riemannian manifolds admitting a one-parameter group of conformal transformations, J. Differential Geometry 4 (1970) 335-337.
28. M. Obata, The conjectures on conformal transformations of Riemannian manifolds, Bull. Amer. Math. Soc. 77 (1971) 265-270.
29. K. Ogiue, Theory of conformal connections, Kōdai Math. Sem. Rep. 19 (1967) 193-224.
30. S. Sternberg, Lectures on differential geometry, Prentice-Hall, Englewood Cliffs, N. J., 1964.
31. N. Tanaka, Conformal connections and conformal transformations, Trans. Amer. Math. Soc. 92 (1959) 168-190.
32. S. Tanno & W. C. Weber, Closed conformal vector fields, J. Differential Geometry 3 (1969) 361-366.
33. Y. Tashiro, Complete Riemannian manifolds and some vector fields, Trans. Amer. Math. Soc. 117 (1965) 251-275.
34. K. Yano, The theory of Lie derivatives and its applications, North-Holland, Amsterdam, 1957.
35. K. Yano & T. Nagano, Einstein spaces admitting a one-parameter group of con formal transformations, Ann. of Math. 69 (1959) 451-461.
36. K. Yano & M. Obata, Sur le groupe de transformations conformes d'une variété de Riemann dont le scalaire de courbure est constant, C. R. Acad. Sci. Paris 260 (1965) 2698-2700.
37. K. Yano & M. Obata, Conformal changes of Riemannian metrics, J. Differential Geometry 4 (1970) 53-92.