Abstract
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].
Original language | English (US) |
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Pages (from-to) | 297-325 |
Number of pages | 29 |
Journal | Commentarii Mathematici Helvetici |
Volume | 77 |
Issue number | 2 |
DOIs | |
State | Published - 2002 |
All Science Journal Classification (ASJC) codes
- General Mathematics
Keywords
- Holomorphic vector field
- Kähler-Ricci soliton
- New holomorphic invariant