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Open AccessArticle

Inaudibility of k-D’Atri Properties

Departamento de Matemáticas, Universidad de Extremadura, Av. de Elvas s/n, 06006 Badajoz, Spain
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Author to whom correspondence should be addressed.
These authors contributed equally to this work.
Symmetry 2019, 11(10), 1316; https://doi.org/10.3390/sym11101316
Received: 9 September 2019 / Revised: 14 October 2019 / Accepted: 17 October 2019 / Published: 20 October 2019
(This article belongs to the Special Issue Geometry of Submanifolds and Homogeneous Spaces)
Working on closed Riemannian manifolds the first author and Schueth gave a list of curvature properties which cannot be determined by the eigenvalue spectrum of the Laplace–Beltrami operator. Following Kac, it is said that such properties are inaudible. Here, we add to that list the dimension of the manifold minus three new properties namely k-D’Atri for k = 3 , , dim M 1 . View Full-Text
Keywords: Laplace operator; isospectral manifolds; geodesic symmetries; D’Atri space; k-D’Atri space; ?ℭ-space Laplace operator; isospectral manifolds; geodesic symmetries; D’Atri space; k-D’Atri space; ?ℭ-space
MDPI and ACS Style

Arias-Marco, T.; Fernández-Barroso, J.M. Inaudibility of k-D’Atri Properties. Symmetry 2019, 11, 1316.

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