论文标题
当地的共形SKT几乎是阿贝利安谎言代数
Locally conformal SKT almost abelian Lie algebras
论文作者
论文摘要
本地的共形SKT（较快的LCSKT）结构是一个Hermitian结构$（J，G）$，其Bismut Torsion 3型$ H $满足条件$ DH =α\ wedge H $，对于某些封闭的非零1型1型$α$。这种情况是在[6]中引入的，作为SKT（或多腔）条件$ DH = 0 $的概括。在本文中，我们描述了几乎是阿贝利安的谎言代数，承认Hermitian结构$（j，g）$，使得$ dh =α\ wedge h $，对于某些封闭的1型$α$。作为申请，我们将LCSKT分类为几乎是Abelian Lie代数为$ 6 $。最后，我们还研究了几乎Abelian Lie代数，LCSKT条件与其他类型的Hermitian结构之间的兼容性。
A locally conformal SKT (shortly LCSKT) structure is a Hermitian structure $(J, g)$ whose Bismut torsion 3-form $H$ satisfies the condition $dH = α\wedge H$, for some closed non-zero 1-form $α$. This condition was introduced in [6] as a generalization of the SKT (or pluriclosed) condition $dH= 0$. In this paper, we characterize the almost abelian Lie algebras admitting a Hermitian structure $(J, g)$ such that $dH = α\wedge H$, for some closed 1-form $α$. As an application we classifiy LCSKT almost abelian Lie algebras in dimension $6$. Finally, we also study on almost abelian Lie algebras the compatibility between the LCSKT condition and other types of Hermitian structures.
