TY - JOUR
T1 - On closed manifolds with harmonic Weyl curvature
AU - Tran, Hung
N1 - Publisher Copyright:
© 2017 Elsevier Inc.
PY - 2017/12/15
Y1 - 2017/12/15
N2 - We derive point-wise and integral rigidity/gap results for a closed manifold with harmonic Weyl curvature in any dimension. In particular, there is a generalization of Tachibana's theorem for non-negative curvature operator. The key ingredients are new Bochner–Weitzenböck–Lichnerowicz type formulas for the Weyl tensor, which are generalizations of identities in dimension four.
AB - We derive point-wise and integral rigidity/gap results for a closed manifold with harmonic Weyl curvature in any dimension. In particular, there is a generalization of Tachibana's theorem for non-negative curvature operator. The key ingredients are new Bochner–Weitzenböck–Lichnerowicz type formulas for the Weyl tensor, which are generalizations of identities in dimension four.
KW - Bochner formula
KW - Harmonic Weyl curvature
KW - Tachibana's theorem
UR - http://www.scopus.com/inward/record.url?scp=85034056009&partnerID=8YFLogxK
U2 - 10.1016/j.aim.2017.10.030
DO - 10.1016/j.aim.2017.10.030
M3 - Article
AN - SCOPUS:85034056009
VL - 322
SP - 861
EP - 891
JO - Advances in Mathematics
JF - Advances in Mathematics
SN - 0001-8708
ER -