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arXiv · 1804.02726

Generic spectrum of warped products and G-manifolds

Marcus A. M. Marrocos·José N. V. Gomes
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Abstract

In this paper, we establish a kind of splitting theorem for the eigenvalues of a specific family of operators on the base of a warped product. As a consequence, we prove a density theorem for a set of warping functions that makes the spectrum of the Laplacian a warped-simple spectrum. This is then used to study the generic situation of the eigenvalues of the Laplacian on a class of compact G-manifolds. In particular, we give a partial answer to a question posed in 1990 by Steven Zelditch about the generic situation of multiplicity of the eigenvalues of the Laplacian on principal bundles.

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BibTeXRIS

Marcus A. M. Marrocos, José N. V. Gomes. 2018-04-08. Generic spectrum of warped products and G-manifolds. https://doi.org/10.1007/s12220-018-00106-x

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