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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

A note on the analytic families
of compact submanifolds
of complex manifolds


Author: Zhiqin Lu
Journal: Proc. Amer. Math. Soc. 128 (2000), 767-774
MSC (1991): Primary 32G05; Secondary 58H15
Published electronically: July 8, 1999
MathSciNet review: 1625769
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Abstract | References | Similar Articles | Additional Information

Abstract: In this paper, we prove a result of the deformation of the complex structure of a submanifold. Our result is a modification of the result of Kodaira (Ann. Math 75(1), 146-162, 1962).


References [Enhancements On Off] (What's this?)

  • 1. K. Kodaira, A theorem of completeness of characteristic systems for analytic families of compact submanifolds of complex manifolds, Ann. of Math. (2) 75 (1962), 146–162. MR 0133841 (24 #A3665b)
  • 2. K. Kodaira and D. C. Spencer, A theorem of completeness of characteristic systems of complete continuous systems, Amer. J. Math. 81 (1959), 477–500. MR 0112156 (22 #3011)
  • 3. Gang Tian, Smoothness of the Universal Deformation Space of Compact Calabi-Yau Manifolds and its Peterson-Weil Metric, Mathematical aspects of string theory, (1), 629-646, Shing-Tung Yau ed, 1987, World Scientific CMP 20:04

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Additional Information

Zhiqin Lu
Email: lu@math.columbia.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-99-05059-5
PII: S 0002-9939(99)05059-5
Keywords: Deformation of the complex structure, Kodaira-Spencer theory, Calabi-Yau manifold
Received by editor(s): January 23, 1998
Received by editor(s) in revised form: April 22, 1998
Published electronically: July 8, 1999
Communicated by: Leslie Saper
Article copyright: © Copyright 1999 American Mathematical Society