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A curvature identity on a 6-dimensional Riemannian manifold and its applications
Czechoslovak Mathematical Journal, Tome 67 (2017) no. 1, pp. 253-270 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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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
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
DOI : 10.21136/CMJ.2017.0540-15
Classification : 53B20, 53C25
Keywords: Chern-Gauss-Bonnet theorem; curvature identity; locally harmonic manifold 
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     title = {A curvature identity on a 6-dimensional {Riemannian} manifold and its applications},
     journal = {Czechoslovak Mathematical Journal},
     pages = {253--270},
     year = {2017},
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     number = {1},
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Euh, Yunhee; Park, Jeong Hyeong; Sekigawa, Kouei. A curvature identity on a 6-dimensional Riemannian manifold and its applications. Czechoslovak Mathematical Journal, Tome 67 (2017) no. 1, pp. 253-270. doi: 10.21136/CMJ.2017.0540-15

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