Abstract
We derive a curvature identity that holds on any 6-dimensional Riemannian manifold, from the Chern-Gauss-Bonnet theorem for a 6-dimensional closed Riemannian manifold. Moreover, some applications of the curvature identity are given. We also define a generalization of harmonic manifolds to study the Lichnerowicz conjecture for a harmonic manifold “a harmonic manifold is locally symmetric” and provide another proof of the Lichnerowicz conjecture refined by Ledger for the 4-dimensional case under a slightly more general setting.
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This research was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education (NRF- 2014R1A1A2053413) and (NRF-2016R1D1A1B03930449).
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Euh, Y., Park, J.H. & Sekigawa, K. A curvature identity on a 6-dimensional Riemannian manifold and its applications. Czech Math J 67, 253–270 (2017). https://doi.org/10.21136/CMJ.2017.0540-15
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DOI: https://doi.org/10.21136/CMJ.2017.0540-15