关于Hijazi不等式和旋量Killing方程的推广的几点注记
Some Remarks on the Hijazi Inequality and Generalizations of the Killing Equation for Spinors
摘要：
推广了Th. Friedrich（1980）和O. Hijazi（1986，1992）. Friedrich/Kim最近构造的Einstein-Dirac方程的特解就是这些不等式的极限情形的例子。这些估计的极限情况的讨论产生两个新的场方程推广的Killing方程以及旋量场的弱Killing方程。最后，我们讨论了2-和3-维的情况下，更详细。
英文摘要：
We generalize the well-known lower estimates for the first eigenvalue of the Dirac operator on a compact Riemannian spin manifold proved by Th. Friedrich (1980) and O. Hijazi (1986, 1992). The special solutions of the Einstein-Dirac equation constructed recently by Friedrich/Kim are examples for the limiting case of these inequalities. The discussion of the limiting case of these estimates yields two new field equations generalizing the Killing equation as well as the weak Killing equation for spinor fields. Finally, we discuss the 2- and 3-dimensional case in more detail.
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