Geodesic
On the spectrum of Riemannian submersions with totally geodesic fibers
Atti della Accademia nazionale dei Lincei. Rendiconti Lincei. Matematica e applicazioni, Série 9, Tome 1 (1990) no. 4, pp. 335-340.

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In this Note we give a rule to compute explicitely the spectrum and the eigenfunctions of the total space of a Riemannian submersion with totally geodesic fibers, in terms of the spectra and eigenfunctions of the typical fiber and any associated principal bundle.
In questa Nota diamo una regola di calcolo esplicito dello spettro e delle autofunzioni dello spazio totale di una submersione riemanniana a fibre totalmente geodetiche, in termini dello spettro e delle autofunzioni della fibra tipo e di un qualsiasi fibrato principale associato. 
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Besson, Gérard; Bordoni, Manlio. On the spectrum of Riemannian submersions with totally geodesic fibers. Atti della Accademia nazionale dei Lincei. Rendiconti Lincei. Matematica e applicazioni, Série 9, Tome 1 (1990) no. 4, pp. 335-340. http://geodesic.mathdoc.fr/item/RLIN_1990_9_1_4_a8/

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