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Article

Euh, Yunhee ; Park, Jeong Hyeong ; Sekigawa, Kouei
A curvature identity on a 6-dimensional Riemannian manifold and its applications. (English). Czechoslovak Mathematical Journal, vol. 67 (2017), issue 1, pp. 253-270
MSC: 53B20, 53C25 | MR 3633010 | Zbl 06738516 | DOI: 10.21136/CMJ.2017.0540-15
Keywords:
Chern-Gauss-Bonnet theorem; curvature identity; locally harmonic manifold
Summary:
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.\looseness -1
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