四维洛伦兹李群上向量场的调和性与极小性
Harmonicity and Minimality of vector fields on four-dimensional Lorentzian lie groups
摘要：
考虑四维李群具有左不变的洛伦兹爱因斯坦度量，并确定了这些空间上向量场的调和性。在某些情况下，所有这些向量场都是能量泛函限于向量场的临界点。我们还对定义调和映射的向量场进行了分类，并明确地计算了这些向量场的能量。然后研究了能量泛函的临界点的极小性。
英文摘要：
We consider four dimensional lie groups equipped with left invariant Lorentzian Einstein metrics, and determine the harmonicity properties of vector fields on these spaces. In some cases, all these vector fields are critical points for the energy functional restricted to vector fields. We also classify vector fields defining harmonic maps, and calculate explicitly the energy of these vector fields. Then we study the minimality of critical points for the energy functional.
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