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Geometry of Kodaira moduli spaces

Author: Sergey A. Merkulov
Journal: Proc. Amer. Math. Soc. 124 (1996), 1499-1506
MSC (1991): Primary 32G10, 32L25, 53B05, 53B10
MathSciNet review: 1327027
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Abstract: A general theorem on the existence of natural torsion-free affine connections on a complete family of compact complex submanifolds in a complex manifold is proved.

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  • 1. T. N. Bailey and R. J. Baston (eds.), Twistors in mathematics and physics, Cambridge University Press, Cambridge, 1990. MR 91k:32033
  • 2. T. N. Bailey and M. G. Eastwood, Complex paraconformal manifolds -- their differential geometry and twistor theory, Forum Math. , 3 (1991), 61--103. MR 92a:32038
  • 3. R. J. Baston and M. G. Eastwood, The Penrose transform, Oxford University Press, Oxford, 1989. MR 92j:32112
  • 4. A. Besse, Einstein manifolds, Springer, Berlin, 1987. MR 88f:53087
  • 5. C. P. Boyer, A note on hyper-Hermitian four-manifolds, Proc. Amer. Math. Soc. 102 (1988), 157--164. MR 89c:53049
  • 6. M. G. Eastwood and C. R. LeBrun, Fattening complex manifolds: curvature and Kodaira-Spencer maps, J. Geom.Phys. ,8 (1992), 123--146. MR 93d:32048
  • 7. S. A. Huggett (ed.), Twistor theory, Marcel Dekker, 1994, to appear. MR 95f:00013
  • 8. N. Hitchin, Complex manifolds and Einstein's equations, In: H. D. Doebner, et al. (eds.) Twistor geometry and non-linear systems, Springer, Berlin, Lect. Notes Math. , vol. 970 (1982), 73--99. MR 84i:32041
  • 9. K. Kodaira, A theorem of completeness of characteristic systems for analytic families of compact submanifolds of complex manifolds, Ann. Math., 75 (1962), 146--162. MR 24:A3665
  • 10. C. LeBrun, Quaternionic-Kähler manifolds and conformal geometry, Math. Ann. , 284 (1989), 353--376. MR 90e:53062
  • 11. Yu. I. Manin, Gauge Field theory and Complex Geometry, Nauka, Moscow 1984.
  • 12. S. A. Merkulov, Moduli of compact submanifolds of complex fibred manifolds, to appear in Math. Proc. Cambridge Phil. Soc.
  • 13. ------, Geometry of relative deformations I, In Twistor theory, Marcel Dekker, 1994, to appear. CMP 95:05
  • 14. S. A. Merkulov and H. Pedersen, Geometry of relative deformations II, In Twistor theory, Marcel Dekker 1994, to appear. CMP 95:05
  • 15. H. Pedersen and Y. S. Poon, Twistorial construction of quaternionic manifolds, In Proc. VIth Int. Coll. on Diff. Geom. , Cursos y Congresos, Univ. Santiago de Compostela, 61 (1989), 207--218. MR 91f:53040
  • 16. H. Pedersen and A. Swann, Riemannian submersions, four-manifolds and Einstein-Weyl geometry, Proc. London Math. Soc. 66 (1993), 381--399. MR 94c:53061
  • 17. R. Penrose, Non-linear gravitons and curved twistor theory, Gen. Rel. Grav. 7 (1976), 31--52. MR 55:11905
  • 18. R. Penrose and W. Rindler, Spinors and space-time, Vol.2, Cambridge University Press, Cambridge, 1986. MR 88b:83003
  • 19. R. S. Ward, On self-dual gauge fields, Phys. Lett. 61A (1977), 81--82. MR 56:2186
  • 20. ------, Self-dual space-times with cosmological constant, Commun. Math. Phys., 78 (1980), 1--17. MR 82g:83004
  • 21. R. S. Ward and R. O. Wells, Jr., Twistor geometry and field theory, Cambridge University Press, Cambridge, 1990. MR 91b:32034

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Additional Information

Sergey A. Merkulov
Affiliation: School of Mathematics and Statistics, University of Plymouth, Plymouth, Devon PL4 8AA, United Kingdom
Address at time of publication: Department of Pure Mathematics, Glasgow University, 15 University Gardens, Glasgow G12 8QW, United Kingdom

Received by editor(s): October 19, 1994
Communicated by: Christopher B. Croke
Article copyright: © Copyright 1996 American Mathematical Society

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