论文标题
$ g_2 $ -type $ t $ roots上的广义标志歧管上的公寓学
Equigeodesics on generalized flag manifolds with $G_2$-type $t$-roots
论文作者
论文摘要
我们研究具有$ g_2 $ -type $ t $ roots $ g/k $ $ g/k $的同质曲线，这是相对于$ g/k $的每个$ g $ invariant度量的大地测量。这些曲线称为公平。这种标志歧管的切线空间分为六个各向同性求和，它们与$ t $ roots是一对一的信件。同样，这些空间是对特殊的全旗歧管$ g_2/t $的概括。我们为具有$ g_2 $ -type $ t $ roots的标志歧管的结构式式进行了特征，我们给出了每个这样的标志歧管，这是一个子空间列表，其中向量是结构性公平向量的子空间。
We study homogeneous curves in generalized flag manifolds $G/K$ with $G_2$-type $t$-roots, which are geodesics with respect to each $G$-invariant metric on $G/K$. These curves are called equigeodesics. The tangent space of such flag manifolds splits into six isotropy summands, which are in one-to-one correspondence with $t$-roots. Also, these spaces are a generalization of the exceptional full flag manifold $G_2/T$. We give a characterization for structural equigeodesics for flag manifolds with $G_2$-type $t$-roots, and we give for each such flag manifold, a list of subspaces in which the vectors are structural equigeodesic vectors.
