TY - JOUR
T1 - Uniqueness of Kähler-Ricci solitons on compact kähler manifolds
AU - Tian, Gang
AU - Xiaohua, Zhu
PY - 1999/12/1
Y1 - 1999/12/1
N2 - We introduce a new holomorphic invariant on any compact Kähler manifolds with positive first Chern class and nontrivial holomorphic vector fields, which contains the Futaki invariant as a special case. This invariant is shown to be an obstruction to the existence of Kähler-Ricci solitons. By solving a complex Monge-Ampère equation, we prove the uniqueness of Kähler-Ricci solitons.
AB - We introduce a new holomorphic invariant on any compact Kähler manifolds with positive first Chern class and nontrivial holomorphic vector fields, which contains the Futaki invariant as a special case. This invariant is shown to be an obstruction to the existence of Kähler-Ricci solitons. By solving a complex Monge-Ampère equation, we prove the uniqueness of Kähler-Ricci solitons.
UR - http://www.scopus.com/inward/record.url?scp=0033426768&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=0033426768&partnerID=8YFLogxK
U2 - 10.1016/S0764-4442(00)88625-5
DO - 10.1016/S0764-4442(00)88625-5
M3 - Article
AN - SCOPUS:0033426768
SN - 0764-4442
VL - 329
SP - 991
EP - 995
JO - Comptes Rendus de l'Academie des Sciences - Series I: Mathematics
JF - Comptes Rendus de l'Academie des Sciences - Series I: Mathematics
IS - 11
ER -