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Isospectral metrics on classical compact simple Lie groups.

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Call No.	Ph.D. 2003
Author	Proctor, Emily B.
Title	Isospectral metrics on classical compact simple Lie groups.
Date	2003
Abstract	We prove the existence of nontrivial multiparameter isospectral deformations of metrics on the classical compact simple Lie groups SO (n) (n = 9, n ≥11), Spin(n) (n = 9, n ≥11), SU (n) (n ≥7), and Sp (n) (n ≥5). The proof breaks into three main steps. First we outline a method devised by Schueth for constructing metrics on these groups from linear maps. Isospectrality and equivalence of linear maps are defined and we invoke a theorem by Schueth which states that isospectral linear maps give rise to isospectral metrics. Next we prove the existence of multidimensional families of linear maps such that within each family the maps are pairwise isospectral and pairwise not equivalent. Finally, we prove that generically, if [Special characters omitted.] is a family of metrics arising from a collection of pairwise nonequivalent linear maps, then for any metric g contained in [Special characters omitted.] there are at most finitely many metrics in [Special characters omitted.] which are isometric to g. Thus we conclude the existence of nontrivial multiparameter isospectral deformations of metrics on the classical compact simple Lie groups of large enough dimension.
Description	vi, 68 leaves : ill. 28 cm.
Format	application/pdf
Advisor	Carolyn S. Gordon.
Subject	Lie groups. ; Spectral geometry. ; Metric spaces. ; Linear operators. ; Riemannian manifolds.
College	Dartmouth College -- Department of Mathematics.
Issuing Body	Dartmouth Dissertations are made available through the Dartmouth Digital Library.
Degree	Thesis (Ph.D.)--Dartmouth College.
Copyright	All rights reserved. No part of this book may be reproduced in any form by any electronic or mechanical means without permission in writing from the author.
DOI	http://dx.doi.org/10.1349/ddlp.1679

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Isospectral metrics on classical compact simple Lie groups.

Isospectral metrics on classical compact simple Lie groups.