Results in Mathematics

, Volume 63, Issue 1–2, pp 107–114 | Cite as

A Curvature Identity on a 4-Dimensional Riemannian Manifold

  • Yunhee Euh
  • JeongHyeong ParkEmail author
  • Kouei Sekigawa


We recall a curvature identity for 4-dimensional compact Riemannian manifolds as derived from the generalized Gauss–Bonnet formula. We extend this curvature identity to non-compact 4-dimensional Riemannian manifolds. We also give some applications of this curvature identity.

Mathematics Subject Classification (2010)

53B20 53C20 


Generalized Gauss–Bonnet formula 3-dimensional curvature identity 


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Copyright information

© Springer Basel AG 2011

Authors and Affiliations

  1. 1.Department of MathematicsSungkyunkwan UniversitySuwonKorea
  2. 2.Department of Mathematics, Faculty of ScienceNiigata UniversityNiigataJapan

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