Complex structures on Riemannian four-manifolds

Mathematische Annalen

Volumn 309, Issue 1, 1997, Pages 159-177

  Pontecorvo, Massimiliano ^a  

^a ROMA TRE UNIVERSITY   (Italy)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0031508258     PISSN: 00255831     EISSN: None     Source Type: Journal    
DOI: 10.1007/s002080050108     Document Type: Article

References (42)

1. [AG] D. V. Alekseevsky, M. M. Graev: Calabi-Yau metric on the Fermat surface. Isometries and totally geodesics submanifolds, J. Geom. Physics 7 (1990) 21-43.
2. [AMP] D.V. Alekseevsky, S. Marchiafava, M. Pontecorvo: In preparation.
3. . [ApG] V. Apostolov, P. Gauduchon: The riemannian Golberg-Sachs theorem, Preprint 1995.
4. [A] N. Aronszajn: A unique continuation theorem for solutions of elliptic partial differential equations or inequalities of the second order, J. Math. Pure Appl. 36 (1957) 235-249.
5. [AHS] M.F. Atiyah, N.J. Hitchin, I.M. Singer: Self-duality in four-dimensional Riemannian geometry , Proc R. Soc. London Ser. A 362 (1978), 425-461
6. [BPV] W. Barth, C. Peters, A. Van de Ven: Compact complex surfaces Berlin Heidelberg New York Tokyo, Springer, 1984.
7. 0 and affine geometry . Math. USSR-Izv 10 (1976), 255-269.
8. [BKW] W.M. Boothby, S. Kobayashi, H.C. Wang: A note on mappings and automorphisms of almost complex manifolds , Ann. of Math. (2) 77 (1963), 329-334.
9. C.P. Boyer: Conformal duality and compact complex surfaces , Math. Ann. 274 (1986), 517-526.
10. C.P. Boyer: A note on hyperhemitian four-manifolds , Proc. Am. Math. Soc. 102 (1988), 157-164.
11. [ES] J. Eells, S. Salamon: Twistorial construction of harmonic maps of surfaces into four-manifolds. Ann. Sc. Norm. Sup. di Pisa 12 (1985), 589-640.
12. 0 with curves , Proc. Japan Acad. Ser. A 56 (1980), 275-279.
13. P. Gauduchon: La 1-forme de torsion d'une variété hermitienne compact. Math. Ann. 267 (1984), 495-518.
14. 3, J. reine angew. Math. 469 (1995), 1-50.
15. [Gr] G. Grantcharov: Private communications.
16. N. Hitchin: Linear field equations on self-dual spaces . Proc. R. Lond. Soc. A 370 (1980), 173-191.
17. N. Hitchin: Kählenan twistor spaces , Proc. Lond. Math. Soc. (3) 43 (1981), 133-150.
18. [K] P. Kobak: Explicit doubly-hermitian metrics , ESI preprint (1995).
19. [KN] S. Kobayashi, K. Nomizu: Foundations of differential geometry. II. Wiley, New York, 1969.
20. [Ko] K. Kodaira: On the structure of compact complex analytic surfaces II , Am. J. Math. 88 (1966), 682-721; III, Am. J. Math. 90 (1968), 55-83.
21. [Ko] K. Kodaira: On the structure of compact complex analytic surfaces II , Am. J. Math. 88 (1966), 682-721; III, Am. J. Math. 90 (1968), 55-83.
22. 2 , J. Diff. Geom. 34 (1991), 223-253.
23. C. LeBrun: Anti-self-dual hermitian metrics on blown-up Hopf surfaces , Math. Ann. 289 (1991), 383-392.
24. C. LeBrun: Polarized 4-manifolds, extremal Kähler metrics an Seiberg-Witten theory, Preprint (1995).
25. 0, Illinois J. Math. 34 (1990), 217-220.
26. J. Li, S.T, Yau, F. Zheng: On projectively-flat hermitian manifolds , Comm. Anal. Geom. 2 (1994), 103-109.
27. A. Lichnerowicz: Géométrie des groupes de transformations Dunod, 1958.
28. D. McDuff: The local behaviour of holomorphic curves in almost complex 4-manifolds, J. Diff. Geom. 34 (1991), 143-164.
29. 0 with curves , Inv. Math. 78 (1984), 393-443.
30. I. Nakamura: Towards classification of nonKähler complex surfaces , Sugaku Expositions 2 (1989), 209-229.
31. [NW] A. Nijenhuis, W. Woolf: Some integration problems in almost-complex and complex manifolds , Ann. of Math. (2) 77 (1963), 424-489.
32. [PT] V. Pidstrigach, A. Tyurin: Invariants of the smooth structures of algebraic surfaces arising from the Dirac operator, Izv. AN SSSR 52:2 (1992), 279-371.
33. M. Pontecorvo: Algebraic dimension of twistor spaces and scalar curvature of anti-self-dual metrics, Math. Ann. 291 (1991), 113-122.
34. M. Pontecorvo: Hermitian surfaces and a twistor space of algebraic dimension 2. Proc. Am. Math. Soc. 113(1991), 177-186.
35. M. Pontecorvo: On twistor spaces of anti-self-dual hermitian surfaces , Trans. Am. Math. Soc. 331 (1992), 653-661.
36. M. Pontecorvo: Uniformization of conformally flat hermitian surfaces , Differential Geometry and its Applications 2 (1992), 295-305.
37. M. Pontecorvo: On the complex geometry of twistor spaces , Seminari di Geometria 1994-1995, Universita' di Bologna, (1996), 195-216
38. [Po] Y.S. Poon: Torus symmetries of compact self-dual manifolds , Geom. Dedicata 60 (1996), 49-64.
39. [S] S. Salamon: Special structures on four-manifolds , Riv. Mat. Univ. Parma (4) 17 (1991), 109-123.
40. e série, t. 11 (1978), 211-228.
41. 0 surfaces, Int. J. Math. 5 (1994), 253-264.
42. [W] E. Witten: Monopoles and four-manifolds , Math. Res. Lett. 1 (1994), 769-796.