Chern–Simons invariants and isometric immersions of warped products

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• 作者：Li Ma (1)
  Jie Zhou (1)
  
• 关键词：Chern–Simons invariant ; Isometric immersion ; Warped product ; Primary 53C40 ; 53C05
• 刊名：Monatshefte f眉r Mathematik
• 出版年：2010
• 出版时间：March 2010
• 年：2010
• 卷：159
• 期：4
• 页码：361-378
• 全文大小：178KB
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• 作者单位：Li Ma (1)
  Jie Zhou (1)
  
  1. Department of Mathematical Sciences, Tsinghua University, 100084, Beijing, People’s Republic of China
  
• ISSN：1436-5081

文摘

In this paper, we calculate the Chern–Simons invariants on some 3-manifolds (e.g., Berger Sphere, warped product 3-manifolds) which obtain particular features in physics. We present the condition such that Berger sphere and warped product 3-manifolds are locally conformally flat. We also give a sufficient and necessary condition such that the warped product 3-manifolds can be isometrically immersed in ${\mathbb{R}^4}$ . The latter condition is different from those in the earlier works of others.