Hermitian conformal classes and almost Kähler structures on 4-manifolds

Differential Geometry and its Application

Volumn 11, Issue 2, 1999, Pages 179-195

  Apostolov, Vestislav ^a   Draghici, Tedi ^b  

^a INSTITUTE OF MATHEMATICS AND INFORMATICS   (Bulgaria)

^b NORTHEASTERN ILLINOIS UNIVERSITY   (United States)

Author keywords

Almost K hler structures; Hermitian conformal classes; Symplectic forms; Yamabe constants

Indexed keywords

EID: 0033197252     PISSN: 09262245     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0926-2245(99)00033-9     Document Type: Article

References (28)

1. D. Alekseevsky and M. Graev, Calabi-Yau metrics on the Fermat surface. Isometries and totally geodesics submanifolds, J. Geom. Phys. 7 (1990) 21-43.
2. V. Apostolov, J. Davidov and O. Muskarov, Compact self-dual hermitian surfaces, Trans. Amer. Math. Soc. 348 (1996) 3051-3063.
3. V. Apostolov and P. Gauduchon, The Riemannian Goldberg-Sachs theorem, Int. J. Math. 8 (1997) 421-439.
4. V. Apostolov, P. Gauduchon and G. Grantcharov, Bihermitian structures on complex surfaces, Proc. London Math. Soc. 79 (1999) 241-248.
5. J. Armstrong, Almost Kähler Einstein 4-manifolds, preprint.
6. A. Balas, Compact hermitian manifolds of constant holomorphic sectional curvature, Math. Z. 189 (1985) 193-210.
7. O. Biquard, Les équations de Seiberg-Witten sur une surface complexe non kählerienne, Comm. Anal. Geom. 6 (1) (1998) 173-197.
8. D. Blair, The isolatedness of special metrics, in: Differential Geometry and its Applications, Proc. Conf. Dubrovnik, 1988 (Univ. Novi Sad, Novi Sad, 1989) 49-58.
9. D. Blair, The "total scalar curvature" as a symplectic invariant, in: Proc. 3rd Congress of Geometry, Thessaloniki, 1991 (Aristotle Univ. Thessaloniki, Thessaloniki, 1992) 79-83.
10. P. Gauduchon, Surfaces kähleriennes dont la courbure vérifie certaines conditions de positivité, in: Bérnard-Bergery, Berger, Houred, eds., Géométrie Riemannienne en Dimension 4, Séminaire A. Besse 1978-1979 (CEDIC/Fernand Nathan, 1981).
11. P. Gauduchon, Fibrés hermitiens à endomorphisme de Ricci non-negatif, Bull. Soc. Math. France 105 (1977) 113-140.
12. P. Gauduchon, Le théorème de l'excetricité nulle, C.R. Acad. Sc. Fr. Serie A (1977) 387-390.
13. P. Gauduchon, La 1-forme de torsion d'une variété hermitienne compacte, Math. Ann. 267 (1984) 495-518.
14. H. Geiges, Symplectic couples on 4-manifolds, Duke Math. J. 85 (1986) 701-711.
15. N. Hitchin, The self-duality equations on a Riemann surface, Proc. London Math. Soc. 55 (3) (1987) 59-126.
16. P. Kobak, Explicit doubly-Hermitian metrics, Diff. Geom. Appl. 10 (1999) 179-185.
17. C. LeBrun, On the scalar curvature of Complex surfaces, Geom. Func. An. 5 (1995) 619-628.
18. C. LeBrun, Yamabe constants and the perturbed Seiberg-Witten equations, Comm. Anal. Geom. 5 (1997) 535-555.
19. A. Lichnerowicz, Géometrie des Groupes de Transformations (Dunod, Paris, 1958).
20. A. Lichnerowicz, Théorie Globale des Connexions et des Groupes D'holonomie (Edizioni Cremonese, Roma, 1962).
21. P. Kronheimer and T. Mrowka, The genus of embedded surfaces in the complex projective space, Math. Res. Lett. 1 (1994) 797-808.
22. T. Oguro and K. Sekigawa, Four-dimensional almost Kähler Einstein and *-Einstein manifolds, Geom. Dedicata 69 (1) (1998) 91-112.
23. M. Pontecorvo, Complex structures on Riemannian four-manifolds, Math. Ann. 309 (1997) 159-177.
24. S. Salamon, Special structures on four-manifolds, Riv. Math. Univ. Parma. 17 (1991) 109-123.
25. R. Shoen, Conformal deformations of Riemannian metrics to constant scalar curvature, J. Diff. Geom. 20 (1984) 479-495.
26. C. Taubes, More constraints on symplectic forms from Seiberg-Witten invariants, Math. Res. Lett. 2 (1995) 9-13.
27. I. Vaisman, Some curvature properties of complex surfaces, Ann. Mat. Purra Appl. 32 (1982) 1-18.
28. S. Yau, On the scalar curvature of compact Hermitian manifolds, Inv. Math. 25 (1974) 213-239.