Advanced Studies in Pure Mathematics

On Deformations of Self-Dual Vector Bundles over Quaternionic Manifolds

James F. Glazebrook and Duraiswamy Sundararaman

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Abstract

In this paper we survey a number of results concerned with the deformations of quaternionic structures on classes of quaternionic manifolds and the deformation theory of Hermitian bundles with self-dual connections. The deformations in question are shown to correspond to the deformation theory of complex structures and holomorphic vector bundles over an associated complex manifold referred to as a twistor space. Results related to hypercomplex and hyperkähler manifolds are also discussed.

Article information

Source
CR-Geometry and Overdetermined Systems, T. Akahori, G. Komatsu, K. Miyajima, M. Namba and K. Yamaguchi, eds. (Tokyo: Mathematical Society of Japan, 1997), 141-157

Dates
Received: 19 October 1995
Revised: 19 August 1996
First available in Project Euclid: 15 August 2018

Permanent link to this document
https://projecteuclid.org/ euclid.aspm/1534361110

Digital Object Identifier
doi:10.2969/aspm/02510141

Mathematical Reviews number (MathSciNet)
MR1476242

Zentralblatt MATH identifier
0893.53009

Citation

Glazebrook, James F.; Sundararaman, Duraiswamy. On Deformations of Self-Dual Vector Bundles over Quaternionic Manifolds. CR-Geometry and Overdetermined Systems, 141--157, Mathematical Society of Japan, Tokyo, Japan, 1997. doi:10.2969/aspm/02510141. https://projecteuclid.org/euclid.aspm/1534361110


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