论文标题
有限体积的伪热均匀空间的刚性
Rigidity of pseudo-Hermitian homogeneous spaces of finite volume
论文作者
论文摘要
令$ m $为有限量的伪 - 温米均匀空间。我们表明，$ m $是紧凑的，并且$ m $的全态同量的身份成分$ g $紧凑。如果仅连接$ m $，那么即使是整体的全体形态同轴法也是紧凑的。这些结果源于对$ M $的山雀纤维的仔细分析，该激发具有圆环作为纤维。证明是基于紧凑的几乎伪 - 温米同质空间的自动形态群体的基础结果。众所周知，根据$ g $的Levi分解，紧凑的均匀伪kähler歧管将其分为复杂的圆环和合理的均质品种。示例表明，紧凑的均匀伪 - 休假歧管通常不会以这种方式分裂。
Let $M$ be a pseudo-Hermitian homogeneous space of finite volume. We show that $M$ is compact and the identity component $G$ of the group of holomorphic isometries of $M$ is compact. If $M$ is simply connected, then even the full group of holomorphic isometries is compact. These results stem from a careful analysis of the Tits fibration of $M$, which is shown to have a torus as its fiber. The proof builds on foundational results on the automorphisms groups of compact almost pseudo-Hermitian homogeneous spaces. It is known that a compact homogeneous pseudo-Kähler manifold splits as a product of a complex torus and a rational homogeneous variety, according to the Levi decomposition of $G$. Examples show that compact homogeneous pseudo-Hermitian manifolds in general do not split in this way.
