Abstract
We prove a classification theorem by cohomology classes for compact Riemannian manifolds with a one-parameter group of isometries without fixed points generalizing the classification of line bundles (more precisely, their circle bundles) over compact manifolds by their first Chern class. We also prove a classification theorem generalizing that of holomorphic line bundles over compact complex manifold by the Picard group of the base for a subfamily of manifolds with additional structure resembling that of circle bundles of such holomorphic line bundles.
The final version of this paper was written while the author was visiting the Department of Mathematics at the University of São Carlos, Brazil, financed by a grant from FAPESP. IIe gratefully acknowledges their hospitality.
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Dedicated to Linda P. Rothschild
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Mendoza, G.A. (2010). Characteristic Classes of the Boundary of a Complex b-manifold. In: Complex Analysis. Trends in Mathematics. Birkhäuser Basel. https://doi.org/10.1007/978-3-0346-0009-5_15
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DOI: https://doi.org/10.1007/978-3-0346-0009-5_15
Publisher Name: Birkhäuser Basel
Print ISBN: 978-3-0346-0008-8
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