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

作者：Euh Yunhee^*; Park Jeong Hyeong; Sekigawa Kouei

来源：Czechoslovak Mathematical Journal, 2017, 67(1): 253-270.

DOI：10.21136/CMJ.2017.0540-15

• Chern-Gauss-Bonnet theorem
• curvature identity
• locally harmonic manifold

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.

• 出版日期2017-3