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A Curvature Identity on a 4-Dimensional Riemannian Manifold

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Abstract

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.

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Authors and Affiliations

  1. Department of Mathematics, Sungkyunkwan University, Suwon, 440-746, Korea

    Yunhee Euh & JeongHyeong Park

  2. Department of Mathematics, Faculty of Science, Niigata University, Niigata, 950-2181, Japan

    Kouei Sekigawa

Authors
  1. Yunhee Euh
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  2. JeongHyeong Park
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  3. Kouei Sekigawa
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Correspondence to JeongHyeong Park.

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Euh, Y., Park, J. & Sekigawa, K. A Curvature Identity on a 4-Dimensional Riemannian Manifold. Results. Math. 63, 107–114 (2013). https://doi.org/10.1007/s00025-011-0164-3

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  • DOI: https://doi.org/10.1007/s00025-011-0164-3

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