A cornucopia of isospectral pairs of metrics on spheres with different local geometries
A cornucopia of isospectral pairs of metrics on spheres with different local geometries
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具有不同局部几何形状的球体上的等谱对度量的聚宝盆
DOI：
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发表时间：
2000
期刊：
影响因子：
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通讯作者：
Z. Szabó
中科院分区：
文献类型：
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作者：
Z. Szabó
本文总结了[Sz5]中开始的全面研究，其中第一个非平凡的等谱度量对是在球和球体上构造的。这些调查包括四种不同的情况下，因为这些球和领域都被认为是2步幂零李群和他们的可解扩展。在[Sz5]的考虑是完全结束在球的情况下，并在幂零的情况下。其他案件主要是概述。本文完全建立了球面上的等谱性定理。本文还总结了可解扩张所需的重要细节。
This article concludes the comprehensive study started in [Sz5], where the first nontrivial isospectral pairs of metrics are constructed on balls and spheres. These investigations incorporate four different cases since these balls and spheres are considered both on 2-step nilpotent Lie groups and on their solvable extensions. In [Sz5] the considerations are completely concluded in the ball-case and in the nilpotent-case. The other cases were mostly outlined. In this paper the isospectrality theorems are completely established on spheres. Also the important details required about the solvable extensions are concluded in this paper.