Geodesic
The Spectral Geometry of Reimannian Submersions
Zbornik radova, Tome 6 (1997) no. 14, p. 36 Cet article a éte moissonné depuis la source eLibrary of Mathematical Institute of the Serbian Academy of Sciences and Arts

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We study the spectral geometry of a Riemannian submersion $\pi : Z -> Y$. We give necessary and sufficient conditions that $\pi$ preserve the eigenforms of the Laplacian. We show that if the pull-back of an eigenform is an eigenform, then the eigenvalue can only increase. If $G$ is a compact, connected Lie group with $H^1(G;R)\neq 0$, we give examples of principal $G$ bundles over homogeneous manifolds where the pull-back of an eigenform from the base is an eigenform on the total space with different eigenvalue. 
@article{ZR_1997_6_14_a3,
     author = {Peter B. Gilkey and John V. Leahy and Jeong Hyeong Park},
     title = {The {Spectral} {Geometry} of {Reimannian} {Submersions}},
     journal = {Zbornik radova},
     pages = {36 },
     year = {1997},
     volume = {6},
     number = {14},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ZR_1997_6_14_a3/}
}
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Peter B. Gilkey; John V. Leahy; Jeong Hyeong Park. The Spectral Geometry of Reimannian Submersions. Zbornik radova, Tome 6 (1997) no. 14, p. 36 . http://geodesic.mathdoc.fr/item/ZR_1997_6_14_a3/