Isospectral manifolds with different local geometries

Simple item page
dc.creatorSchueth, Dorothee
dc.date2001-02-16
dc.date.accessioned2026-07-07T04:40:12Z
dc.date.available2026-07-07T04:40:12Z
dc.descriptionWe construct several new classes of isospectral manifolds with different local geometries. After reviewing a theorem by Carolyn Gordon on isospectral torus bundles and presenting certain useful specialized versions (Chapter 1) we apply these tools to construct the first examples of isospectral four-dimensional manifolds which are not locally isometric (Chapter 2). Moreover, we construct the first examples of isospectral left invariant metrics on compact Lie groups (Chapter 3). Thereby we also obtain the first continuous isospectral families of globally homogeneous manifolds and the first examples of isospectral manifolds which are simply connected and irreducible. Finally, we construct the first pairs of isospectral manifolds which are conformally equivalent and not locally isometric (Chapter 4).
dc.description59 pages, AMS-TeX. Habilitation thesis (2000), to appear in: J. Reine Angew. Math
dc.identifierhttps://arxiv.org/abs/math/0102123
dc.identifierhttp://arxiv.org/abs/math/0102123
dc.identifierJ. Reine Angew. Math. 534 (2001), 41 - 94
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/60951
dc.subjectDifferential Geometry
dc.subjectSpectral Theory
dc.subject58J53
dc.titleIsospectral manifolds with different local geometries
dc.typetext

Files

Collections

arXiv