On the decomposition of conformally flat manifolds

Hiroyasu IZEKI

doi:10.2969/jmsj/04510105

Hiroyasu IZEKI

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ジャーナルフリー

1993 年 45 巻 1 号 p. 105-119

DOI https://doi.org/10.2969/jmsj/04510105

詳細

Published: 1993 Received: 1991/12/27 Available on J-STAGE: 2006/10/20 Accepted: - Advance online publication: - Revised: -
訂正情報
訂正日: 2006/10/20 訂正理由: - 訂正箇所: 引用文献情報訂正内容: Wrong : 1) T. Aubin, Equation différentielles non linéaires et problèmes de Yamabe concernant la courbure scalaire, J. Math. Pures Appl., 55 (1976), 269-296.
2) J. P. Bourguignon, Les variétés de dimension 4 à signature non nulle dont la courbure est harmonique sont d'Einstein, Invent. Math., 63 (1981), 263-286.
3) M. Brown, A proof of the generalized Schoenflies theorem, Bull. Amer. Math. Soc., 66 (1960), 74-76.
4) R. E. Gompf, Killing the Akbulut-Kirby 4-sphere, with relevance to the Andrews-Curtis and Schoenflies problems, Topology, 30 (1991), 97-115.
5) M. Gromov and H. B. Lawson, Spin and scalar curvature in the presence of a fundamental group I, Ann. of Math., 111 (1980), 209-230.
6) M. Gromov and H. B. Lawson, Positive scalar curvature and the Dirac operator on complete Riemannian manifolds, Publ. Math. IHES, 58 (1983), 295-408.
7) D. Johnson and J. J. Millson, Deformation spaces associated to compact hyperbolic manifolds, Discrete Groups in Geometry and Analysis, (ed. R. Howe), Progr. Math., 67, Birkhäuser, Boston, 1987.
8) O. Kobayashi, A Willmore type problem for S²×S², Lecture Notes in Math., 1255, Springer, Berlin-Heidelberg, 1987.
9) O. Kobayashi, Scalar curvature of a metric with unit volume, Math. Ann., 279 (1987), 253-265.
10) O. Kobayashi, On the Yamabe problem (in Japanese), Sem. Math. Sc., 16, Dept. Math. Keio Univ., 1990.
11) N. H. Kuiper, On conformally flat spaces in the large, Ann. of Math., 50 (1949), 916-924.
12) R. S. Kulkarni, On the principle of uniformization, J. Differential Geom., 13 (1978), 109-138.
13) R. S. Kulkarni and U. Pinkall, Uniformizations of geometric structures and applications to conformal geometry, Lecture Notes in Math., 1209, Springer, Berlin-Heidelberg, 1986.
14) J. Lafontaine, Remarque sur les variétés conformément plates, Math. Ann., 259 (1982), 313-319.
15) J. M. Lee and T. H. Parker, The Yamabe problem, Bull. Amer. Math. Soc., 17 (1987), 37-91.
16) J. W. Milnor, A unique decomposition theorem for 3-manifolds, Amer. J. Math., 84 (1962), 1-7.
17) R. Schoen, Conformal deformation of a Riemannian metric to constant scalar curvatures, J. Differential Geom., 20 (1984), 479-495.
18) R. Schoen and S. T. Yau, On the structure of manifolds with positive scalar curvature, Manuscripta Math., 28 (1979), 159-183.
19) R. Schoen and S. T. Yau, Conformally flat manifolds, Kleinian groups and scalar curvature, Invent. Math., 92 (1988), 47-71.
20) N. S. Trudinger, Remarks concerning the conformal deformation of Riemannian structures on compact manifolds, Ann. Scuola Norm. Sup. Pisa, ser. 3, 22 (1963), 265-274.
21) H. Yamabe, On a deformation of Riemannian structures on compact manifolds, Osaka Math. J., 12 (1960), 21-37.

Right : [1] T. Aubin, Equation différentielles non linéaires et problèmes de Yamabe concernant la courbure scalaire, J. Math. Pures Appl., 55 (1976), 269-296.
[2] J. P. Bourguignon, Les variétés de dimension 4 à signature non nulle dont la courbure est harmonique sont d'Einstein, Invent. Math., 63 (1981), 263-286.
[3] M. Brown, A proof of the generalized Schoenflies theorem, Bull. Amer. Math. Soc., 66 (1960), 74-76.
[4] R. E. Gompf, Killing the Akbulut-Kirby 4-sphere, with relevance to the Andrews-Curtis and Schoenflies problems, Topology, 30 (1991), 97-115.
[5] M. Gromov and H. B. Lawson, Spin and scalar curvature in the presence of a fundamental group I, Ann. of Math., 111 (1980), 209-230.
[6] M. Gromov and H. B. Lawson, Positive scalar curvature and the Dirac operator on complete Riemannian manifolds, Publ. Math. IHES, 58 (1983), 295-408.
[7] D. Johnson and J. J. Millson, Deformation spaces associated to compact hyperbolic manifolds, Discrete Groups in Geometry and Analysis, (ed. R. Howe), Progr. Math., 67, Birkhäuser, Boston, 1987.
[8] O. Kobayashi, A Willmore type problem for S²×S², Lecture Notes in Math., 1255, Springer, Berlin-Heidelberg, 1987.
[9] O. Kobayashi, Scalar curvature of a metric with unit volume, Math. Ann., 279 (1987), 253-265.
[10] O. Kobayashi, On the Yamabe problem (in Japanese), Sem. Math. Sc., 16, Dept. Math. Keio Univ., 1990.
[11] N. H. Kuiper, On conformally flat spaces in the large, Ann. of Math., 50 (1949), 916-924.
[12] R. S. Kulkarni, On the principle of uniformization, J. Differential Geom., 13 (1978), 109-138.
[13] R. S. Kulkarni and U. Pinkall, Uniformizations of geometric structures and applications to conformal geometry, Lecture Notes in Math., 1209, Springer, Berlin-Heidelberg, 1986.
[14] J. Lafontaine, Remarque sur les variétés conformément plates, Math. Ann., 259 (1982), 313-319.
[15] J. M. Lee and T. H. Parker, The Yamabe problem, Bull. Amer. Math. Soc., 17 (1987), 37-91.
[16] J. W. Milnor, A unique decomposition theorem for 3-manifolds, Amer. J. Math., 84 (1962), 1-7.
[17] R. Schoen, Conformal deformation of a Riemannian metric to constant scalar curvatures, J. Differential Geom., 20 (1984), 479-495.
[18] R. Schoen and S. T. Yau, On the structure of manifolds with positive scalar curvature, Manuscripta Math., 28 (1979), 159-183.
[19] R. Schoen and S. T. Yau, Conformally flat manifolds, Kleinian groups and scalar curvature, Invent. Math., 92 (1988), 47-71.
[20] N. S. Trudinger, Remarks concerning the conformal deformation of Riemannian structures on compact manifolds, Ann. Scuola Norm. Sup. Pisa, ser. 3, 22 (1963), 265-274.
[21] H. Yamabe, On a deformation of Riemannian structures on compact manifolds, Osaka Math. J., 12 (1960), 21-37.

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