TY - JOUR
T1 - A new holomorphic invariant and uniqueness of Kähler-Ricci solitons
AU - Tian, Gang
AU - Zhu, Xiaohua
PY - 2002
Y1 - 2002
N2 - In this paper, a new holomorphic invariant is defined on a compact Kähler manifold with positive first Chern class and nontrivial holomorphic vector fields. This invariant generalizes the Futaki invariant. We prove that this invariant is an obstruction to the existence of Kähler-Ricci solitons. In particular, using this invariant together with the main result in [TZ1], we solve completely the uniqueness problem of Kähler-Ricci solitons. Two functionals associated to the new holomorphic invariant are also discussed. The main result here was announced in [TZ2].
AB - In this paper, a new holomorphic invariant is defined on a compact Kähler manifold with positive first Chern class and nontrivial holomorphic vector fields. This invariant generalizes the Futaki invariant. We prove that this invariant is an obstruction to the existence of Kähler-Ricci solitons. In particular, using this invariant together with the main result in [TZ1], we solve completely the uniqueness problem of Kähler-Ricci solitons. Two functionals associated to the new holomorphic invariant are also discussed. The main result here was announced in [TZ2].
KW - Holomorphic vector field
KW - Kähler-Ricci soliton
KW - New holomorphic invariant
UR - http://www.scopus.com/inward/record.url?scp=0036444098&partnerID=8YFLogxK
U2 - 10.1007/s00014-002-8341-3
DO - 10.1007/s00014-002-8341-3
M3 - Article
SN - 0010-2571
VL - 77
SP - 297
EP - 325
JO - Commentarii Mathematici Helvetici
JF - Commentarii Mathematici Helvetici
IS - 2
ER -