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Holomorphic Frames for Weakly Converging Holomorphic Vector Bundles

Published online by Cambridge University Press:  20 November 2018

Georgios D. Daskalopoulos  and
Richard A. Wentworth
Georgios D. Daskalopoulos
Affiliation:
Department of Mathematics, Brown University, Providence, RI 02912, U.S.A. e-mail: [email protected]
Richard A. Wentworth
Affiliation:
Department of Mathematics, Johns Hopkins University, Baltimore, MD 21218, U.S.A. e-mail: [email protected]
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Abstract

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Using a modification of Webster's proof of the Newlander–Nirenberg theorem, it is shown that, for a weakly convergent sequence of integrable unitary connections on a complex vector bundle over a complex manifold, there is a subsequence of local holomorphic frames that converges strongly in an appropriate Holder class.

Keywords

57M5058E2053C24
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 49 , Issue 1 , 01 March 2006 , pp. 36 - 40
Copyright
Copyright © Canadian Mathematical Society 2006

References

[K] Kobayashi, S., Differential Geometry of Complex Vector Bundles. Publications of the Mathematical Society of Japan 15, Princeton University Press, Princeton, NJ, 1987.Google Scholar
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[W] Webster, S., A new proof of the Newlander-Nirenberg theorem. Math. Z. 201(1989), 303–316.Google Scholar