منابع مشابه
Isospectral locally symmetric manifolds
In this article we construct closed, isospectral, non-isometric locally symmetric manifolds. We have three main results. First, we construct arbitrarily large sets of closed, isospectral, non-isometric manifolds. Second, we show the growth of size these sets of isospectral manifolds as a function of volume is super-polynomial. Finally, we construct pairs of infinite towers of finite covers of a...
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We give quantitive estimates for the number of locally symmetric spaces of a given type with bounded volume. Explicitly, let S be a symmetric space of non-compact type without Euclidean de Rham factors. Then, after rescaling appropriately the Riemannian metric, the following hold. Theorem A If rank(S) = 1 and S ≇ H2,H3, then there are at most V V Riemannian manifolds, locally isometric to S, wi...
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Given two isospectral not isometric manifolds, we construct a new couple of such manifolds as the total spaces of two Riemannian submersions with totally geodesic fibers isometric to the given ones and of basis any other given manifold. By iteration, we obtain families of isospectral not isometric manifolds.
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In this paper we construct, for n ≥ 2, arbitrarily large families of infinite towers of compact, orientable Riemannian n-manifolds which are isospectral but not isometric at each stage. In dimensions two and three, the towers produced consist of hyperbolic 2-manifolds and hyperbolic 3-manifolds, and in these cases we show that the isospectral towers do not arise from Sunada’s method.
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ژورنال
عنوان ژورنال: Indiana University Mathematics Journal
سال: 2014
ISSN: 0022-2518
DOI: 10.1512/iumj.2014.63.5242