We construct the first examples of continuous families of isospectral Riemannian metrics that are not locally isometric on closed manifolds , more precisely, on , where is a torus of dimension and is a sphere of dimension . These metrics are not locally homogeneous; in particular, the scalar curvature of each metric is nonconstant. For some of the deformations, the maximum scalar curvature changes during the deformation.
On construit les premiers exemples de familles continues de métriques riemanniennes isospectrales, mais pas localement isométriques sur des variétés fermées, plus précisément sur , où est un tore de dimension et est une sphère de dimension . Ces métriques ne sont pas localement homogènes ; en particulier, la courbure scalaire d’une telle métrique n’est pas constante. Dans certaines des déformations que l’on considère, la courbure scalaire maximale change pendant la déformation.
@article{AIF_1998__48_2_593_0, author = {Gordon, Carolyn S. and Gornet, Ruth and Schueth, Dorothee and Webb, David L. and Wilson, Edward N.}, title = {Isospectral deformations of closed riemannian manifolds with different scalar curvature}, journal = {Annales de l'Institut Fourier}, pages = {593--607}, publisher = {Association des Annales de l{\textquoteright}institut Fourier}, volume = {48}, number = {2}, year = {1998}, doi = {10.5802/aif.1630}, mrnumber = {99b:53049}, zbl = {0922.58083}, language = {en}, url = {http://www.numdam.org/articles/10.5802/aif.1630/} }
TY - JOUR AU - Gordon, Carolyn S. AU - Gornet, Ruth AU - Schueth, Dorothee AU - Webb, David L. AU - Wilson, Edward N. TI - Isospectral deformations of closed riemannian manifolds with different scalar curvature JO - Annales de l'Institut Fourier PY - 1998 SP - 593 EP - 607 VL - 48 IS - 2 PB - Association des Annales de l’institut Fourier UR - http://www.numdam.org/articles/10.5802/aif.1630/ DO - 10.5802/aif.1630 LA - en ID - AIF_1998__48_2_593_0 ER -
%0 Journal Article %A Gordon, Carolyn S. %A Gornet, Ruth %A Schueth, Dorothee %A Webb, David L. %A Wilson, Edward N. %T Isospectral deformations of closed riemannian manifolds with different scalar curvature %J Annales de l'Institut Fourier %D 1998 %P 593-607 %V 48 %N 2 %I Association des Annales de l’institut Fourier %U http://www.numdam.org/articles/10.5802/aif.1630/ %R 10.5802/aif.1630 %G en %F AIF_1998__48_2_593_0
Gordon, Carolyn S.; Gornet, Ruth; Schueth, Dorothee; Webb, David L.; Wilson, Edward N. Isospectral deformations of closed riemannian manifolds with different scalar curvature. Annales de l'Institut Fourier, Volume 48 (1998) no. 2, pp. 593-607. doi : 10.5802/aif.1630. http://www.numdam.org/articles/10.5802/aif.1630/
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