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Flat bundles and hyper-Hodge decomposition on solvmanifolds. (English) Zbl 1327.53065
Summary: We study rank 1 flat bundles over solvmanifolds whose cohomologies are nontrivial. By using Hodge theoretical properties for all topologically trivial rank 1 flat bundles, we represent the structure theorem of Kähler solvmanifolds as extensions of Hasegawa’s result and Benson-Gordon’s result for nilmanifolds.

MSC:
53C30 Differential geometry of homogeneous manifolds
22E25 Nilpotent and solvable Lie groups
58A14 Hodge theory in global analysis
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