Energy Properness and Sasakian-Einstein Metrics
Energy Properness and Sasakian-Einstein Metrics
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DOI：
10.1007/s00220-011-1292-z
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发表时间：
2010-07
影响因子：
2.4
通讯作者：
Xi Zhang
中科院分区：
文献类型：
--
作者：
Xi Zhang
本文证明了Sasakian-Einstein度规的存在与相应能量泛函的适定性密切相关。在不允许非平凡的哈密顿全纯向量场的条件下，证明了Sasakian-Einstein度规的存在蕴含着Moser-Trudinger型不等式。在本文的最后，我们还得到了Sasakian几何中的一个Miyaoka-Yau型不等式。
In this paper, we show that the existence of Sasakian-Einstein metrics is closely related to the properness of corresponding energy functionals. Under the condition of admitting no nontrivial Hamiltonian holomorphic vector field, we prove that the existence of Sasakian-Einstein metric implies a Moser-Trudinger type inequality. At the end of this paper, we also obtain a Miyaoka-Yau type inequality in Sasakian geometry.