Czechoslovak Mathematical Journal, Vol. 67, No. 1, pp. 253-270, 2017
A curvature identity on a 6-dimensional Riemannian manifold and its applications
Yunhee Euh, Jeong Hyeong Park, Kouei Sekigawa
Received October 9, 2015. First published February 24, 2017.
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.
Affiliations: Yunhee Euh, Department of Mathematical Sciences, Seoul National University, 1 Gwanak-ro, Gwanak-gu, Seoul 08826, Korea e-mail: email@example.com; Jeong Hyeong Park, Department of Mathematics, Sungkyunkwan University, 2066, Seobu-ro, Jangan-gu, Suwon 16419, Gyeong Gi-Do, Korea, e-mail: firstname.lastname@example.org; Kouei Sekigawa, Department of Mathematics, Niigata University, 8050, Ikarashi 2-no-cho, Nishi-ku, Niigata 950-2181, Japan, e-mail: email@example.com