论文标题
紧凑的半简单谎言组的Cyt和SKT指标
CYT and SKT Metrics on Compact Semi-Simple Lie Groups
论文作者
论文摘要
A Hermitian metric on a complex manifold $(M, I)$ of complex dimension $n$ is called Calabi-Yau with torsion (CYT) or Bismut-Ricci flat, if the restricted holonomy of the associated Bismut connection is contained in ${\rm SU}(n)$ and it is called strong Kähler with torsion (SKT) or pluriclosed if the associated fundamental form $F$ is $ \ partial \ overline \ part $ clucted。在论文中，我们研究了紧凑型半简单谎言组的剩余skt和Cyt指标的存在，并带有萨梅森复合物结构$ i $。特别是，我们表明，如果$ i $由某些最大的圆环$ t $和$ g $确定，则是左右的Hermitian度量标准，在Torus $ t $的正确动作下也是cyt and SKT的不变，然后$ G $必须是Bimismut Flat。
A Hermitian metric on a complex manifold $(M, I)$ of complex dimension $n$ is called Calabi-Yau with torsion (CYT) or Bismut-Ricci flat, if the restricted holonomy of the associated Bismut connection is contained in ${\rm SU}(n)$ and it is called strong Kähler with torsion (SKT) or pluriclosed if the associated fundamental form $F$ is $\partial \overline \partial$-closed. In the paper we study the existence of left-invariant SKT and CYT metrics on compact semi-simple Lie groups endowed with a Samelson complex structure $I$. In particular, we show that if $I$ is determined by some maximal torus $T$ and $g$ is a left-invariant Hermitian metric, which is also invariant under the right action of the torus $T$, and is both CYT and SKT, then $g$ has to be Bismut flat.
