TY - JOUR
T1 - The weyl tensor of gradient Ricci solitons
AU - Cao, Xiaodong
AU - Tran, Hung
N1 - Publisher Copyright:
© 2016, Mathematical Sciences Publishers. All rights reserved.
PY - 2016/2/29
Y1 - 2016/2/29
N2 - This paper derives new identities for the Weyl tensor on a gradient Ricci soliton, particularly in dimension four. First, we prove a Bochner–Weitzenböck-type formula for the norm of the self-dual Weyl tensor and discuss its applications, including connections between geometry and topology. In the second part, we are concerned with the interaction of different components of Riemannian curvature and (gradient and Hessian of) the soliton potential function. The Weyl tensor arises naturally in these investigations. Applications here are rigidity results.
AB - This paper derives new identities for the Weyl tensor on a gradient Ricci soliton, particularly in dimension four. First, we prove a Bochner–Weitzenböck-type formula for the norm of the self-dual Weyl tensor and discuss its applications, including connections between geometry and topology. In the second part, we are concerned with the interaction of different components of Riemannian curvature and (gradient and Hessian of) the soliton potential function. The Weyl tensor arises naturally in these investigations. Applications here are rigidity results.
UR - http://www.scopus.com/inward/record.url?scp=84960119405&partnerID=8YFLogxK
U2 - 10.2140/gt.2016.20.389
DO - 10.2140/gt.2016.20.389
M3 - Article
AN - SCOPUS:84960119405
SN - 1465-3060
VL - 20
SP - 389
EP - 436
JO - Geometry and Topology
JF - Geometry and Topology
IS - 1
ER -