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arXiv 0704.0210math.DG
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超势分类

Classification of superpotentials

Andrew Dancer, Mckenzie Wang

摘要:

我们推广了我们以前对上齐性Ricci平坦方程的“数量曲率型”超势的分类。我们现在考虑我们以前的论文中没有涉及的情况,即,当超势的某个权向量位于与主轨道的数量曲率函数相关联的权向量的凸包(的缩放平移)之外时。在这种情况下,我们证明了各向同性表示最多有3个不可约和项,或者超势的一阶子系统与Fano Kähler-Einstein乘积上复线丛上浸没型度规的Calabi-Yau条件具有相同的形式.

英文摘要:

We extend our previous classification of superpotentials of ``scalar curvature type" for the cohomogeneity one Ricci-flat equations. We now consider the case not covered in our previous paper, i.e., when some weight vector of the superpotential lies outside (a scaled translate of) the convex hull of the weight vectors associated with the scalar curvature function of the principal orbit. In this situation we show that either the isotropy representation has at most 3 irreducible summands or the first order subsystem associated to the superpotential is of the same form as the Calabi-Yau condition for submersion type metrics on complex line bundles over a Fano Kähler-Einstein product.

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