On the metric structure of non-Kähler complex surfaces

Mathematische Annalen

Volumn 317, Issue 1, 2000, Pages 1-40

  Belgun, Florin Alexandru ^a  

^a ECOLE POLYTECHNIQUE   (France)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0034384410     PISSN: 00255831     EISSN: None     Source Type: Journal    
DOI: 10.1007/s002080050357     Document Type: Article

References (41)

1. W. Barth, C. Peters, A. Van de Ven, Compact complex surfaces, Ergebnisse der Mathematik und ihrer Grenzgebiete, 3. Folge, Band 4, Springer-Verlag, 1984.
2. F. Belgun, Normal CR structures on compact three-manifolds, preprint.
3. D.E. Blair, Contact manifolds in Riemannian geometry. Lecture Notes in Math. 509, Springer-Verlag, 1976.
4. 0 and affine geometry, Math. USSR Izvestiya 21 (1983), 31-73.
5. N. Buchdahl, On compact Kahler surfaces, Ann. Inst. Fourier 49 (1999), 287-302.
6. L.A. Cordero, L.C. De Andres, M. Fernandez, M. De Leon, Examples of four dimensional locally conformal Kähler manifolds, Geometriae Dedicata 29 (1989), 227-233.
7. L.A. Cordero, M. Fernandez, M. De Leon, Compact locally conformal Kähler nilmanifolds, Geometriae Dedicata 21 (1986), 187-192.
8. S. Dragomir, L. Ornea, Locally conformal Kähler geometry, Birkhäuser 1998.
9. P. Gauduchon, La 1-forme de torsion d'une variété hermitienne compacte, Math. Ann. 267 (1984), 495-518.
10. P. Gauduchon, Complex Structures on Compact Conformal Manifolds of Negative Type, in Complex Analysis and Geometry (Trento), Lecture Notes in Pure and Appl. Math. 173, 201-212.
11. P. Gauduchon, L. Ornea, Locally conformally Kähler metrics on Hopf surfaces, Ann. Inst. Fourier. 48 (1998), 1107-1127.
12. H. Geiges, Normal contact structures on 3-manifolds, Tôhoku Math. J. 49 (1997), 415-422.
13. R. Harvey, H. Blaine Lawson, Jr., An intrinsic characterisation of Kähler manifolds, Inv. Math. 74 (1983), 139-150.
14. 0, Inv. Math. 24 (1974), 269-310.
15. M. Inoue, S. Kobayashi, T. Ochiai, Holomorphic affine connections on compact complex surfaces, J. Fac. Sci. Univ. Tokyo 27 (1980), 247-264.
16. Y. Kamishima, Uniformization of compact complex surfaces by locally conformal Kähler structure, Preprint.
17. Y. Kamishima, T. Tsuboi, C R structures on Seifert manifolds, Inv. Math. 104 (1991), 149-163.
18. Ma. Kato, Topology of Hopf surfaces, J. Math. Soc. Japan 27 (1975), 222-238; Erratum to "Topology of Hopf surfaces", J. Math. Soc. Japan 41 (1989), 173-174.
19. Ma. Kato, Topology of Hopf surfaces, J. Math. Soc. Japan 27 (1975), 222-238; Erratum to "Topology of Hopf surfaces", J. Math. Soc. Japan 41 (1989), 173-174.
20. B. Klingler, Structures affines et projectives sur les surfaces complexes, Ann. Inst. Fourier 48 (1998), 441-477.
21. S. Kobayashi, K. Nomizu, Foundations of differential geometry I, Interscience Publishers, New York.
22. K. Kodaira, On compact complex analytic spaces I, Ann. Math. 71 (1960), 111-152; II, ibid. 77 (1963), 563-626; III, ibid. 78 (1963), 1-40.
23. K. Kodaira, On compact complex analytic spaces I, Ann. Math. 71 (1960), 111-152; II, ibid. 77 (1963), 563-626; III, ibid. 78 (1963), 1-40.
24. K. Kodaira, On compact complex analytic spaces I, Ann. Math. 71 (1960), 111-152; II, ibid. 77 (1963), 563-626; III, ibid. 78 (1963), 1-40.
25. K. Kodaira, On the structure of compact complex analytic spaces I, Am. J. Math. 86 (1964), 751 -798; II, ibid. 88 ( 1966), 682-721; III, ibid. 90 (1969), 55-83; IV, ibid. 90 (1969), 1048-1066.
26. K. Kodaira, On the structure of compact complex analytic spaces I, Am. J. Math. 86 (1964), 751 -798; II, ibid. 88 ( 1966), 682-721; III, ibid. 90 (1969), 55-83; IV, ibid. 90 (1969), 1048-1066.
27. K. Kodaira, On the structure of compact complex analytic spaces I, Am. J. Math. 86 (1964), 751 -798; II, ibid. 88 ( 1966), 682-721; III, ibid. 90 (1969), 55-83; IV, ibid. 90 (1969), 1048-1066.
28. K. Kodaira, On the structure of compact complex analytic spaces I, Am. J. Math. 86 (1964), 751 -798; II, ibid. 88 ( 1966), 682-721; III, ibid. 90 (1969), 55-83; IV, ibid. 90 (1969), 1048-1066.
29. C.R. Lebrun, Anti-self-dual Hermitian metrics on blown-up Hopf surfaces., Math. Ann 289 (1991), 383-392.
30. K. Maehara, On elliptic surfaces whose first Betti numbers are odd, Int. Symp. on Alg. Geom., Kyoto (1977), 565-574.
31. M. Namba, Automorphism groups of Hopf surfaces, Tohoku math. J., II Ser. 26 (1974), 133-157.
32. P. Scott, The geometries of 3-manifolds, Bull. London Math. Soc. 15 (1983), 401-487.
33. Y.-T. Siu, Every K3 surface is Kähler, Inv. Math. 73 (1983), 139-150.
34. 2 by affine transformation groups, J. Diff. Geometry 10 (1975), 239-252.
35. F. Tricerri, Some examples of locally conformal Kähler manifolds, Rend. Semin. Mat. Univ. Politecn. Torino 40 (1982), 81-92.
36. F. Tricerri, I. Vaisman, On some 2-dimensional Hermitian manifolds, Math. Zeitschrift 192 (1986), 205-216.
37. I. Vaisman, Locally conformal Kähler manifolds with parallel Lee form, Rendiconti di Matematica, Roma 12 (1979), 263-284.
38. I. Vaisman, Non-Kähler metrics on geometric complex surfaces, Rend. Sem. Mat. Univ. Politecn. Torino 45 (1987), 117-123.
39. I. Vaisman, Generalized Hopf manifolds, Geometriae Dedicata 13 (1982), 231-255.
40. Al Vitter, Affine structures on compact complex manifolds, Inv. Math. 17 (1972), 231-244.
41. C.T.C. Wall, Geometric structures on compact complex analytic manifolds, Topology 25 (1986), 119-153.