This article is cited in 6 papers

Local audibility of a hyperbolic metric

V. A. Sharafutdinov

Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences

Abstract: A Riemannian metric $g$ on a compact boundaryless manifold is said to be locally audible if the following statement is true for every metric $g'$ sufficiently close to $g$: if $g$ and $g'$ are isospectral then they are isometric. The local audibility is proved of a metric of constant negative sectional curvature.

Keywords: spectral geometry, Riemannian manifold of negative sectional curvature.

UDC: 515.168+517.984.5

Received: 23.03.2009

 English version: Siberian Mathematical Journal, 2009, 50:5, 929–944

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