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Journal of Geometry

, Volume 103, Issue 2, pp 247–261 | Cite as

Curvatures properties of Lie hypersurfaces in the complex hyperbolic space

  • Tatsuyoshi Hamada
  • Yuji Hoshikawa
  • Hiroshi TamaruEmail author
Article
  • 155 Downloads

Abstract

A Lie hypersurface in the complex hyperbolic space is a homogeneous real hypersurface without focal submanifolds. The set of all Lie hypersurfaces in the complex hyperbolic space is bijective to a closed interval, which gives a deformation of homogeneous hypersurfaces from the ruled minimal one to the horosphere. In this paper, we study intrinsic geometry of Lie hypersurfaces, such as Ricci curvatures, scalar curvatures, and sectional curvatures.

Mathematics Subject Classification (2010)

53C40 53C30 53C35 22E25 

Keywords

Real hypersurfaces complex hyperbolic spaces solvable Lie groups Ricci curvatures scalar curvatures sectional curvatures 

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Copyright information

© Springer Basel 2012

Authors and Affiliations

  • Tatsuyoshi Hamada
    • 1
    • 2
  • Yuji Hoshikawa
    • 3
    • 4
  • Hiroshi Tamaru
    • 3
    Email author
  1. 1.Department of Applied MathematicsFukuoka UniversityFukuokaJapan
  2. 2.JST, CRESTChiyoda-kuJapan
  3. 3.Department of MathematicsHiroshima UniversityHigashi-HiroshimaJapan
  4. 4.Takamatsu-Kita Junior High SchoolTakamatsuJapan

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