Isospectral deformations of closed riemannian manifolds with different scalar curvature
Annales de l'Institut Fourier, Tome 48 (1998) no. 2, p. 593-607
On construit les premiers exemples de familles continues de métriques riemanniennes isospectrales, mais pas localement isométriques sur des variétés fermées, plus précisément sur S n ×T m , où T m est un tore de dimension m2 et S n est une sphère de dimension n4. 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.
We construct the first examples of continuous families of isospectral Riemannian metrics that are not locally isometric on closed manifolds , more precisely, on S n ×T m , where T m is a torus of dimension m2 and S n is a sphere of dimension n4. 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.
@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},
     publisher = {Association des Annales de l'institut Fourier},
     volume = {48},
     number = {2},
     year = {1998},
     pages = {593-607},
     doi = {10.5802/aif.1630},
     zbl = {0922.58083},
     mrnumber = {99b:53049},
     language = {en},
     url = {http://www.numdam.org/item/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, Tome 48 (1998) no. 2, pp. 593-607. doi : 10.5802/aif.1630. https://www.numdam.org/item/AIF_1998__48_2_593_0/

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