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Non existence de structures Kaehleriennes sur le fibres principaux en tores

Bouyakoub, Abdelkader (2005) Non existence de structures Kaehleriennes sur le fibres principaux en tores. Rendiconti del Seminario della Facoltà di Scienze dell'Università di Cagliari, 75 (1-2). pp. 1-7. ISSN 0370727X

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Abstract

The main results of this paper concerns principal circle bundles P with non vanishing Euler class, over odd-dimensional, closed, oriented and connected bases B. Such manifolds do not admit any Kaehler structure. We show that the same holds for principal torus bundles whose characteristic classes span a subgroup of, at least, rank one in the second integral cohomology group of the base space. This approach provides a new proof of a theorem of Benson and Gordon which asserts that no nilmanifold but the torus can be made kaehlerian. We end this note by extending this last result to certain classes of compact solvmanifolds.

Item Type:Article
Date:2005
Institution:Universita' degli Studi di Cagliari
Divisions:Centri > Seminario Scientifico della Facolta' di Scienze MM.FF.NN.
Subjects:Area 01 - Scienze matematiche e informatiche > MAT/03 Geometria
Uncontrolled Keywords:Kaehler structure, Euler class, Theorem of Gordon and Benson, Torus
ID Code:95
Deposited On:03 Nov 2008 11:17

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