论文标题
与H可溶解谎言代数的超复合Nilmanifolds中的复杂曲线
Complex curves in hypercomplex nilmanifolds with H-solvable Lie algebras
论文作者
论文摘要
如果$ i^2 = -ID $，而$ \ sqrt {-1} $ - eigenspace $ a^{1,0,0} $是$ i^2 = -id $，则操作员$ i $ $ $ a $称为复杂的结构操作员。 Lie代数$ A $上的超复杂结构是满足Quaternionic Ressption的$ a $的复杂结构$ i，j $和$ k $的三倍。如果存在Quaternionic-Invaric-Invarianiant子代数的有限过滤，我们称其为二极管 - 季节性可溶性，我们称之为超卵形季节性可溶性，并具有可接合的亚质量为零。我们给出了nilpotent Lie代数上的Quaternion-solvenic-solvenig-solvenig-sypyplex结构的例子，并猜想nilpotent lie代数上的所有超复合结构都是四元离子化的。令$（n，i，j，k）$为与Quaternionic-Solviens-Solvens-solvens-hyperclex lie代数相关的紧凑型超复杂的尼尔曼叶。我们证明，对于四季度引起的一般复杂结构$ l $，在复杂的歧管$（n，l）$中没有复杂的曲线。
An operator $I$ on a real Lie algebra $A$ is called a complex structure operator if $I^2=-Id$ and the $\sqrt{-1}$-eigenspace $A^{1,0}$ is a Lie subalgebra in the complexification of $A$. A hypercomplex structure on a Lie algebra $A$ is a triple of complex structures $I,J$ and $K$ on $A$ satisfying the quaternionic relations. We call a hypercomplex nilpotent Lie algebra quaternionic-solvable if there exists a finite filtration by quaternionic-invariant subalgebras with commutative subquotients which converges to zero. We give examples of quaternionic-solvable hypercomplex structures on a nilpotent Lie algebra and conjecture that all hypercomplex structures on nilpotent Lie algebras are quaternionic-solvable. Let $(N,I,J,K)$ be a compact hypercomplex nilmanifold associated to an quaternionic-solvable hypercomplex Lie algebra. We prove that, for a general complex structure $L$ induced by quaternions, there are no complex curves in a complex manifold $(N,L)$.
