A note on compact solvmanifolds with Kahler structures
A note on compact solvmanifolds with Kahler structures
复制标题
关于具有卡勒结构的紧凑求解流形的注释
DOI：
10.18910/11990
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发表时间：
2004
影响因子：
0.4
通讯作者：
K. Hasegawa
中科院分区：
文献类型：
--
作者：
K. Hasegawa
本文证明紧解流形承认k结构当且仅当它是复环面的有限商，且复环面上具有复环束结构。特别地，我们可以证明完全可解型紧解流形具有k结构当且仅当它是复环面，这被称为Benson-Gordon定理。
In this note we show that a compact solvmanifold admits a Kstructure if and only if it is a finite quotient of a complex torus which has a structure of a com- plex torus bundle over a complex torus. We can show in particular that a compact solvmanifold of completely solvable type has a Kstructure if and only if it is a complex torus, which is known as the Benson-Gordon's conje cture.