We study when the pull-back of an eigenform of the Laplacian on the base of a compact Riemannian $V$-submersion is an eigenform of the Laplacian on the total space of the submersion, and when the associated eigenvalue can change.
@article{1140727070,
author = {Gilkey, Peter and Kim, Hong-Jong and Park, JeongHyeong},
title = {Eigenforms of the Laplacian for Riemannian V-submersions},
journal = {Tohoku Math. J. (2)},
volume = {57},
number = {1},
year = {2005},
pages = { 505-519},
language = {en},
url = {http://dml.mathdoc.fr/item/1140727070}
}
Gilkey, Peter; Kim, Hong-Jong; Park, JeongHyeong. Eigenforms of the Laplacian for Riemannian V-submersions. Tohoku Math. J. (2), Tome 57 (2005) no. 1, pp. 505-519. http://gdmltest.u-ga.fr/item/1140727070/