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Sur le spectre des fibrés en tore qui s'effondrent

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Abstract.

 We consider torus bundles over S 1 and T 2 with solmanifold structure, and analyze the behavior of the Laplacian acting on left-invariant differantial forms under homogeneous collapsings with bounded diameter and bounded sectional curvature. Whe show how the number of small eigenvalues depends on the topology of the bundle and the geometry of the collapsing.

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  1. Institut de mathématiques, Université de Neuchâtel, Rue Émile Argand 11, C.P. 2 CH-2007 Neuchâtel, Suisse. e-mail: pierre.jammes@unine.ch, , , , , , CH

    Pierre Jammes

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  1. Pierre Jammes
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Received: 14 January 2002

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Jammes, P. Sur le spectre des fibrés en tore qui s'effondrent. manuscripta math. 110, 13–31 (2003). https://doi.org/10.1007/s00229-002-0291-y

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  • DOI: https://doi.org/10.1007/s00229-002-0291-y

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