Generic Spectrum of Warped Products and G-Manifolds

Author(s)

Marrocos, Marcus A. M. ^[1] ; Gomes, Jose N. V. ^{[2, 3]}

Affiliation

^[1] Univ Fed ABC, CMCC, Ave Estados, 5001, BR-09210580 Santo Andre, SP - Brazil

^[2] Univ Fed Amazonas, Dept Matemat, Ave Gen Rodrigo Octavio, 6200, BR-69080900 Manaus, AM - Brazil

^[3] Lehigh Univ, Dept Math, Christmas Saucon Hall, 14 East Packer Ave, Bethlehem, PA 18015 - USA

• Document type: Journal article
• Source: JOURNAL OF GEOMETRIC ANALYSIS; v. 29, n. 4, p. 3124-3134, DEC 2019.
• Web of Science Citations: 0

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. (AU)

• FAPESP's process: 16/10009-3 - On eigenvalues of Laplacian in kahler manifolds
• Grantee: Marcus Antonio Mendonça Marrocos
• Support Opportunities: Scholarships abroad - Research