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On a generalization of the hopf fibration, III (Subvarieties in theC-spaces)

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Abstract

Analytic subvarieties inC-spaces are discussed. First, a certain kind of closed 2-formdω is constructed. Then, the subvarieties are studied by means of this 2-form.dω may be considered as the curvature form of a connection whenC-spaces are considered as the toral bundle space over an algebraic variety. This 2-form is horizontal in its nature with respect to the bundle structure and indicates, in general, how different the bundle is from the trivial bundle. Because of this twist in the bundle space, subvarieties in theC-spaces tend to inherit the same structure. In this paper, the inherited fibration structure is studied. The most concrete results are obtained when the fiber torus has complex dimension 2.

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Authors and Affiliations

  1. Department of Mathematics, University of Connecticut, 06268, Storrs, CT, USA

    Kinetsu Abe

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  1. Kinetsu Abe
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Research in part supported by Sonderforschungsbereich, Universität Bonn, 1980–81.

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Abe, K. On a generalization of the hopf fibration, III (Subvarieties in theC-spaces). Monatshefte für Mathematik 99, 169–198 (1985). https://doi.org/10.1007/BF01295153

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  • DOI: https://doi.org/10.1007/BF01295153

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