A curvature identity on a 6-dimensional Riemannian manifold and its applications

Euh, Yunhee   ; Park, Jeong Hyeong   ; Sekigawa, Kouei

Czechoslovak Mathematical Journal, Tome 67 (2017) no. 1, pp. 253-270

Abstract (VO)

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

Détail

DOI : 10.21136/CMJ.2017.0540-15

Classification : 53B20, 53C25
Keywords: Chern-Gauss-Bonnet theorem; curvature identity; locally harmonic manifold

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