论文标题
可整合的谐波希格斯捆绑包，消失的$ \ mathcal {u} $和$ \ mathcal {q} $的eigenvalues
Integrable Harmonic Higgs Bundles With Vanishing $\mathcal{U}$ And Eigenvalues of $\mathcal{Q}$
论文作者
论文摘要
我们研究了tt* - 几何形状，具有消失的胎态$ \ mathcal {u} $。给定一个可以集成的谐波higgs束$（e，h，φ，\ nathcal {u}，\ nathcal {q}）$在复杂的歧管$ m $上，首先，我们首先证明，在\ emph {is}条件下，在\ emph {is}条件下，消失了$ \ nathcal {u} $ nimities $ nimmit $ quins $ nimit $φ $ h $是一个全态连接，因此公制$ h $和$ \ nathcal {q} $是不变的。其次，如果没有\ emph {is}条件，我们表明消失的$ \ nathcal {u} $将暗示消失的higgs field $φ$，如果我们假设$ h $的chern连接是holomorphic的连接。最后，我们添加了真实的结构$κ$。给定任何\ emph {cv} - 结构，我们证明超级对称运算符$ \ mathcal {q} $必须具有$ 0 $作为特征值，当基础捆绑包具有奇数等级。
We study the tt*-geometry with vanishing endormorphism $\mathcal{U}$. Given an integrable harmonic Higgs bundle $(E, h, Φ, \mathcal{U},\mathcal{Q})$ on a complex manifold $M$, Firstly we prove that, under the \emph{IS} condition, vanishing $\mathcal{U}$ implies vanishing Higgs field $Φ$ and the Chern connection of the Hermitian Einstein metric $h$ is a holomorphic connection, so the metric $h$ and $\mathcal{Q}$ are invariant. Secondly, without the \emph{IS} condition, we show that vanishing $\mathcal{U}$ will imply vanishing Higgs field $Φ$ if we assume that the Chern connection of $h$ is a holomorphic connection. Finally, we add real structure $κ$. Given any \emph{CV}-structure, we prove that super-symmetric operator $\mathcal{Q}$ must have $0$ as an eigenvalue when the underlying bundle has odd rank.
