Primitive geodesic lengths and ( almost ) arithmetic progressions 1 Primitive geodesic lengths and ( almost ) arithmetic progressions
Primitive geodesic lengths and ( almost ) arithmetic progressions 1 Primitive geodesic lengths and ( almost ) arithmetic progressions
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原始测地线长度和（几乎）算术级数1 原始测地线长度和（几乎）算术级数
DOI：
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发表时间：
2014
期刊：
影响因子：
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通讯作者：
D. McReynolds
中科院分区：
文献类型：
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作者：
J.;D. McReynolds
本文研究了黎曼流形上的本原测地线长度集何时具有任意长的算术级数。我们证明，在空间中的负弯曲的度量，度量有这样的算术级数是相当罕见的。我们引进几乎算术级数，算术级数的粗糙化，并证明了每一个负弯曲，封闭的黎曼流形有任意长的几乎算术级数在其原始长度谱。关于真算术级数，我们证明了每个非紧算术双曲2-或3-流形在其本原长度谱中具有任意长的算术级数。最后，我们用原始长度谱中的算术级数来描述算术性。我们还给出了一个著名的谱ridigity问题的基础上的算术级数流形的稀缺性的方法。
In this article, we investigate when the set of primitive geodesic lengths on a Riemannian manifold have arbitrarily long arithmetic progressions. We prove that in the space of negatively curved metrics, a metric having such arithmetic progressions is quite rare. We introduce almost arithmetic progressions, a coarsification of arithmetic progressions, and prove that every negatively curved, closed Riemannian manifold has arbitrarily long almost arithmetic progressions in its primitive length spectrum. Concerning genuine arithmetic progressions, we prove that every noncompact arithmetic hyperbolic 2– or 3–manifold has arbitrarily long arithmetic progressions in its primitive length spectrum. We end with a conjectural characterization of arithmeticity in terms of arithmetic progressions in the primitive length spectrum. We also give an approach to a well known spectral ridigity problem based on the scarcity of manifolds with arithmetic progressions.
原始测地线长度和（几乎）算术级数
DOI：
10.5565/publmat6311906
发表时间：
2019
期刊：
Publicacions Matemàtiques
影响因子：
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作者：
Lafont, Jean-François;McReynolds, David Ben
通讯作者：
McReynolds, David Ben