Complex structures on real product bundles with applications to differential geometry
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- by Richard S. Millman PDF
- Trans. Amer. Math. Soc. 166 (1972), 71-99 Request permission
Abstract:
The purpose of this paper is to classify holomorphic principal fibre bundles which admit a smooth section (i.e. are real product bundles). This is accomplished if the structure group is solvable of type (E). In the general case, a sufficient condition is obtained for a real product bundle to be equivalent to the complex product bundle. A necessary and sufficient condition for the existence of a holomorphic connection on a real product bundle is also obtained. Using this criterion in the case where the structure group is abelian, a generalization of a theorem due to Atiyah (in the case the structure group is ${C^ \ast }$) is obtained.References
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Additional Information
- © Copyright 1972 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 166 (1972), 71-99
- MSC: Primary 32L05; Secondary 53C10, 58A10
- DOI: https://doi.org/10.1090/S0002-9947-1972-0302943-3
- MathSciNet review: 0302943