We study exact metrics on non-compact manifolds with exceptional holonomy Spin(7), G_2.W e derive the metrics by using the formulation with vector fields. We point out that the coordinates on coset spaces are useful to handle the metrics. The coset construction also ensures that the metrics are the solutions of the self-duality condition for the spin connection. Then we conjecture the classification of spaces R * G/H with Spin(7) holonomy. Finally, we comment on the coset construction of metrics with SU(3) holonomy.
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机译：我们研究了非紧凑的歧管上的确切度量，具有特殊的正生旋转（7），G_2.WE通过使用矢量字段的配方来推导指标。我们指出了Coset空间的坐标可用于处理指标。陪芯结构还确保度量是自旋连接的自二元状况的解决方案。然后我们猜测Space R * G / H的分类，旋转（7）正常。最后，我们评论了Su（3）种本的核心标准。
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