Compact scalar-flat indefinite Kähler surfaces with Hamiltonian S 1-symmetry

Communications in Mathematical Physics

Volumn 254, Issue 1, 2005, Pages 23-44

  Kamada, Hiroyuki ^a,b  

^a NUMAZU COLLEGE OF TECHNOLOGY   (Japan)

^b MIYAGI UNIVERSITY OF EDUCATION   (Japan)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 12944291378     PISSN: 00103616     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00220-004-1241-1     Document Type: Article

References (25)

1. Barth, W., Peters, C., Van de Ven, A.: Compact complex surfaces. Berlin-Heidelberg-New York-Springer-Verlag, 1984
2. Bott, R.: A residue formula for holomorphic vector fields. J. Differ. Geom. 1, 311-330 (1967)
3. Frankel, T.: Fixed points and torsion on Kähler manifolds. Ann. of Math. II 70, 1-8 (1959)
4. Futaki, A., Mabuchi, T.: Moment maps and symmetric multilinear forms associated with integral symplectic classes. Asian J. Math. 6, 349-372 (2002)
5. Kamada, H.: Indefinite analogue of hyperbolic ansatz and its application. Proceedings of The Fifth Pacific Rim Geometry Conference (Sendai, 2000), Tohoku Mathematical Publications 20, Sendai: Tohoku University Mathematical Institute, 2001, pp. 69-73
6. Kamada, H.: Self-dual Kähler metrics of neutral signature on complex surfaces. Tohoku Mathematical Publications 24, Sendai: Tohoku University, 2002
7. Kamada, H., Machida, Y.: Self-duality of metrics of type (2, 2) on four-dimensional manifolds. Tôhoku Math. J. II, 49, 259-275 (1997)
8. Kazdan, J. L., Warner, F. W.: Curvature function for open 2-manifolds. Ann. of Math. II, 99, 203-219 (1974)
9. Kobayashi, S.: Transformation groups in differential geometry. Berlin-Heidelberg-New York: Springer-Verlag, 1972
10. Kobayashi, S., Nomizu, K.: Foundations of differential geometry, I, II. New York-London: Interscience Publishers, 1963, 1969
11. Kuiper, N. H.: On conformally-flat spaces in the large. Ann. of Math. II, 50, 916-924 (1949)
12. 2. J. Differ. Geom. 34, 223-253 (1991)
13. LeBrun, C.: Kodaira dimension and the Yamabe problem. Comm. Anal. Geom. 7, 133-156 (1999)
14. Matsushita, Y., Law, P.: Hitchin-Thorpe type inequalities for pseudo-Riemannian 4-manifolds of metric signature (++--). Geom. Dedicata 87, 65-89 (2001)
15. McDuff, D.: The moment map for circle actions on symplectic manifolds. J. Geom. Phys. 5, 149-160 (1988)
16. Moser, J.: On the volume elements on a manifold. Trans. Am. Math. Soc. 120, 286-294 (1965)
17. Nakagawa, Y.: Bando-Calabi-Futaki characters of Kähler orbifolds. Math. Ann. 314, 369-380 (1999)
18. Nakagawa, Y.: Bando-Calabi-Futaki character of compact toric manifolds. Tohoku Math. J. 53, 479-490 (2001)
19. Ooguri, H., Vafa, C.: Geometry of N = 2 strings. Nuclear Phys. B 361, 469-518 (1991)
20. Petean, J.: Indefinite Kähler-Einstein metrics on compact complex surfaces. Commun. Math. Phys. 189, 227-235 (1997)
21. Poon, Y. S.: Compact self-dual manifolds with positive scalar curvature. J. Differ. Geom. 24, 97-132 (1986)
22. Qin, Z.: Complex structures on certain differentiable 4-manifolds. Topology 32, 551-566 (1993)
23. Taubes, C. H.: The Seiberg-Witten invariants and symplectic forms. Math. Res. Lett. 1, 809-822 (1994)
24. Tian, G.: Kähler-Einstein metrics on algebraic manifolds. In: Transcendental methods in algebraic geometry (Cetraro, 1994), Lecture Notes in Math. 1646, Berlin: Springer, 1996, pp. 143-185
25. Wolf, J. A.: Spaces of constant curvature. 5th ed., Houston, TX: Publish or Perish, Inc., 1984