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    Bielawski, Roger 2003. Complexification and Hypercomplexification of Manifolds with a Linear Connection. International Journal of Mathematics, Vol. 14, Issue. 08, p. 813.
    Schwachhöfer, Lorenz J. 2001. Connections with Irreducible Holonomy Representations. Advances in Mathematics, Vol. 160, Issue. 1, p. 1.
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Moduli spaces of compact complex submanifolds of complex fibered manifolds

  • Sergey A. Merkulov (a1)
Extract

In 1962 Kodaira[11] proved that ifX ↪ Y is a compact complex submanifold with normal bundle N such that H1(X, N) = 0, then X belongs to a locally complete family {Xt: t ∈ M} of complex submanifolds Xt of Y with the moduli space M being a (dimcH0(X, N))-dimensional complex manifold, and there exists a canonical isomorphism

between the tangent space of M at a point t ∈ M and the space of all global sections of the normal bundle Nt of the embedding Xt ↪ Y.

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COPYRIGHT: © Cambridge Philosophical Society 1995
References
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[1]Ambrose, W. and Singer, I. M.. A theorem on holonomy. Trans. Amer. Math. Soc. 79 (1953), 428–443.
[2]Bailey, T. N. and Eastwood, M. G.. Complex paraconformal manifolds – their differential geometry and twistor theory. Forum Math. 3 (1991), 61–103.
[3]Boyer, C. P.. A note on hyperhermitian four-manifolds. Proc. Amer. Math. Soc. 102 (1988), 157–164.
[4]Bryant, R.. Two exotic holonomies in dimension four, path geometries, and twistor theory. Proc. Symposia in Pure Mathematics 83 (1991), 33–88.
[5]Curtis, W. D., Lerner, D. E. and Miller, F. R.. Complex pp waves and the nonlinear graviten construction. J. Math. Phys. 19 (1978), 2024–2027.
[6]Eastwood, M. G. and LeBrun, C. R.. Fattening complex manifolds: curvature and Kodaira-Spencer maps. J. Geom. Phys. 8 (1992), 123–146.
[7]Grauert, H. and Remmert, R.. Coherent analytic sheaves (Springer, 1984).
[8]Griffiths, P. A.. The extension problem in complex analysis II: embeddings with positive normal bundle. Amer. J. Math. 88 (1966), 366–446.
[9]Hitchin, N. J., Karlhede, A., LindströM, U. and Roček, M.. HyperKähler metrics and supersymmetry. Commun. Math. Phys. 108 (1987), 535–589.
[10]Kobayashi, S. and Nomizu, K.. Foundations of differential geometry, vol. II (Wiley, 1969).
[11]Kodaira, K.. A theorem of completeness of characteristic systems for analytic families of compact submanifolds of complex manifolds. Ann. Math. 75 (1962), 146–162.
[12]Kodaira, K.. Complex manifolds and deformations of complex structures (Springer, 1986).
[13]Pedersen, H. and Swann, A.. Riemannian submersions, four-manifolds and Einstein-Weyl geometry. Proc. London Math. Soc. 66 (1993), 381–399.
[14]Penrose, R.. Nonlinear gravitons and curved twistor theory. Gen. Bel. Grav. 7 (1976), 31–52.
[15]Salamon, S. M.. Differential geometry of quaternionic manifolds. Ann. Scient. EC. Norm. Sup. 4e série, 19 (1986), 31–55.
[16]Tod, K. P. and Ward, R. S.. Self-dual metrics with self-dual Killing vectors. Proc. R. Soc. Lond. A 368 (1979), 411–427.
[17]Ward, R. S.. A class of self-dual solutions of Einstein's equations. Proc. R. Soc. Lond. A 363 (1978), 289–295.
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Mathematical Proceedings of the Cambridge Philosophical Society
  • ISSN: 0305-0041
  • EISSN: 1469-8064
  • URL: /core/journals/mathematical-proceedings-of-the-cambridge-philosophical-society
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