The index of symmetry of compact naturally reductive spaces

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• 作者：Carlos Olmos (1)
  Silvio Reggiani (1)
  Hiroshi Tamaru (2)
  
• 关键词：Index of symmetry ; Distribution of symmetry ; Naturally reductive space ; Symmetric space ; 53C30 ; 53C35
• 刊名：Mathematische Zeitschrift
• 出版年：2014
• 出版时间：August 2014
• 年：2014
• 卷：277
• 期：3-4
• 页码：611-628
• 全文大小：246 KB
• 参考文献：1. Alekseevskii, D.V. (originator): Reductive space. Encyclopedia of Mathematics, http://www.encyclopediaofmath.org/index.php?title=Reductive_space&oldid=11232
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• 作者单位：Carlos Olmos (1)
  Silvio Reggiani (1)
  Hiroshi Tamaru (2)
  
  1. Facultad de Matem谩tica, Astronom铆a y F铆sica, Universidad Nacional de C贸rdoba, Ciudad Universitaria, 5000聽, C贸rdoba, Argentina
  2. Department of Mathematics, Hiroshima University, 1-3-1 Kagamiyama, Higashi-Hiroshima, 739-8526, Japan
  
• ISSN：1432-1823

文摘

We introduce a geometric invariant that we call the index of symmetry, which measures how far is a Riemannian manifold from being a symmetric space. We compute, in a geometric way, the index of symmetry of compact naturally reductive spaces. In this case, the so-called leaf of symmetry turns out to be of the group type. We also study several examples where the leaf of symmetry is not of the group type. Interesting examples arise from the unit tangent bundle of the sphere of curvature 2, and two metrics in an Aloff-Wallach 7-manifold and the Wallach 24-manifold.