Asymptotically Locally Euclidean Metrics with Holonomy SU(m)

Annals of Global Analysis and Geometry

Volumn 19, Issue 1, 2001, Pages 55-73

  Joyce, Dominic ^a  

^a UNIVERSITY OF OXFORD   (United Kingdom)

Author keywords

Asymptotically locally Euclidean; Calabi conjecture; Ricci flat

Indexed keywords

EID: 0002309139     PISSN: 0232704X     EISSN: None     Source Type: Journal    
DOI: 10.1023/A:1006622430781     Document Type: Article

References (23)

1. Bando, S., Kasue, A. and Nakajima, H.: On a construction of coordinates at infinity on manifolds with fast curvature decay and maximal volume growth, Invent. Math. 97 (1989), 313-349.
2. Bando, S. and Kobayashi, R.: Ricci-flat Kähler metrics on affine algebraic manifolds, in: Lecture Notes in Math. 1339, Springer-Verlag, New York, 1988, pp. 20-31.
3. Bando, S. and Kobayashi, R.: Ricci-flat Kähler metrics on affine algebraic manifolds. II, Math. Ann. 287 (1990), 175-180.
4. Besse, A. L.: Einstein Manifolds, Springer-Verlag, New York, 1987.
5. Calabi, E.: On Kähler manifolds with vanishing canonical class, in R. H. Fox, D. C. Spencer and A. W. Tucker (eds), Algebraic Geometry and Topology, A Symposium in Honour of S. Lefschetz, Princeton University Press, Princeton, NJ, 1957, pp. 78-89.
6. Calabi, E.: Métriques kählériennes et fibrés holomorphes, Ann. Sci. École Norm. Sup. 12 (1979), 269-294.
7. Chaljub-Simon, A. and Choquet-Bruhat, Y.: Problèmes elliptiques du second ordre sur une variété euclidienne à l'infini, Ann. Fac. Sci. Toulouse 1 (1978), 9-25.
8. Eguchi, T. and Hanson, A. J.: Asymptotically flat solutions to Euclidean gravity, Phys. Lett. B 74 (1978), 249-251.
9. Gibbons, G. W. and Hawking, S. W.: Gravitational multi-instantons, Phys. Lett. B 78 (1978), 430-432.
10. Gilbarg, D. and Trudinger, N. S.: Elliptic Partial Differential Equations of Second Order, Grundlehren Math. Wiss. 224, Springer-Verlag, Berlin, Berlin, 1977.
11. Joyce, D. D.: Compact 8-manifolds with holonomy Spin(7), Inv. Math. 123 (1996), 507-552.
12. 2. I and II, J. Differential Geom. 43 (1996), 291-328 and 329-375.
13. Joyce, D. D.: Compact Manifolds with Special Holonomy, Math. Monogr. Ser., Oxford University Press, Oxford, 2000, to appear.
14. Joyce, D.: Quasi-ALE metrics with holonomy SU(m) and Sp(m), Ann. Global Anal. Geom. 19, 2001, to appear.
15. Kronheimer, P. B.: The construction of ALE spaces as hyperkähler quotients, J. Differential Geom. 29 (1989), 665-683.
16. Kronheimer, P. B.: A Torelli-type theorem for gravitational instantons, J. Differential Geom. 29 (1989), 685-697.
17. Lee, J. M. and Parker, T. H.: The Yamabe problem, Bull. Amer. Math. Soc. 17 (1987), 37-91.
18. Reid, M.: Young person's guide to canonical singularities, in S. J. Bloch (ed.), Algebraic Geometry, Bowdoin 1985, Proc. Symp. Pure Math. 46, Amer. Math. Soc., Providence, RI, 1987 pp. 345-416.
19. Salamon, S. M.: Riemannian Geometry and Holonomy Groups, Pitman Res. Notes in Math. 201, Longman, Harlow, 1989.
20. Schlessinger, M.: Rigidity of quotient singularities, Invent. Math. 14 (1971), 17-26.
21. Tian, G. and Yau, S.-T.: Complete Kähler manifolds with zero Ricci curvature. I, J. Amer. Math. Soc. 3 (1990), 579-609.
22. Tian, G. and Yau, S.-T.: Complete Kähler manifolds with zero Ricci curvature. II, Invent. Math. 106 (1991), 27-60.
23. Yau, S.-T.: On the Ricci curvature of a compact Kähler manifold and the complex Monge-Ampère equations. I, Comm. Pure Appl. Math. 31 (1978), 339-411.