Journal of the Mathematical Society of Japan

Holomorphic vertical line bundle of the twistor space over a quaternionic manifold

Toshimasa KOBAYASHI

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Abstract

The vertical bundle of the twistor fibration over a 4-dimensional self-dual manifold is a holomorphic line bundle and plays an important role in a study of the twistor space. On the other hand, the vertical bundle of the twistor space over a quaternionic manifold is not a holomorphic line bundle, in general. We shall give the condition for a vertical bundle to be a holomorphic line bundle.

Article information

Source
J. Math. Soc. Japan, Volume 52, Number 3 (2000), 485-499.

Dates
First available in Project Euclid: 10 June 2008

Permanent link to this document
https://projecteuclid.org/euclid.jmsj/1213107282

Digital Object Identifier
doi:10.2969/jmsj/05230485

Mathematical Reviews number (MathSciNet)
MR1760600

Zentralblatt MATH identifier
0995.53036

Subjects
Primary: 53C07: Special connections and metrics on vector bundles (Hermite-Einstein- Yang-Mills) [See also 32Q20]
Secondary: 53C10: $G$-structures 53C15: General geometric structures on manifolds (almost complex, almost product structures, etc.)

Keywords
Quaternionic manifold twistor space Obata connection

Citation

KOBAYASHI, Toshimasa. Holomorphic vertical line bundle of the twistor space over a quaternionic manifold. J. Math. Soc. Japan 52 (2000), no. 3, 485--499. doi:10.2969/jmsj/05230485. https://projecteuclid.org/euclid.jmsj/1213107282


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