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ISSN 1088-6826(e) ISSN 0002-9939(p)

On holomorphic isometric embeddings of the unit disk into polydisks

Author(s): Sui-Chung Ng
Journal: Proc. Amer. Math. Soc. 138 (2010), 2907-2922.
MSC (2010): Primary 53C35, 53C55
Posted: March 19, 2010
MathSciNet review: 2644903
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Abstract | References | Similar articles | Additional information

Abstract: We study the classification of holomorphic isometric embeddings of the unit disk into polydisks. As a corollary of our results, we can give a complete classification when the target is the 2-disk and the 3-disk. We also prove that the holomorphic isometric embeddings between polydisks are induced by those of the unit disk into polydisks.

References:

[E.53]: Calabi, E., Isometric imbedding of complex manifolds, Ann. of Math. (2) 58 (1953), no. 2, 1-23. MR 0057000 (15:160c)
[LE03]: Clozel, L. and Ullmo, E., Correspondances modulaires et mesures invariantes, J. Reine Angew. Math. 558 (2003), 47-83. MR 1979182 (2005a:11056)
[N.a]: Mok, N., Erratum to ``Local holomorphic isometric embeddings arising from correspondences in the rank- case'', 2005, http://hkumath.hku.hk/ $\sim$ nmok/Erratum.pdf.
[N.b]: -, Local holomorphic isometric embeddings arising from correspondences in the rank- case, Contemporary Trends in Algebraic Geometry and Algebraic Topology (Chern, S.S., Fu, L., and Hain, R., eds.), Nankai Tracts in Mathematics, Vol. 5, World Scientific, New Jersey, 2002, pp. 155-166. MR 1945359 (2003k:32032)
[N.ng]: -, Extension of germs of holomorphic isometries up to normalization constants with respect to the Bergman metric, preprint, http://hkumath.hku. hk/ $\sim$ imr/IMRPreprintSeries/ 2009/IMR2009-9.pdf.

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Additional Information:

Sui-Chung Ng
Affiliation: Department of Mathematics, The University of Hong Kong, Pokfulam Road, Hong Kong
Email: math.scng@hku.hk

DOI: 10.1090/S0002-9939-10-10305-0
PII: S 0002-9939(10)10305-0
Received by editor(s): July 30, 2009
Received by editor(s) in revised form: November 27, 2009
Posted: March 19, 2010
Communicated by: Richard A. Wentworth
Copyright of article: Copyright 2010, American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.

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