赋形算子上的Rarita-Schwinger型算子
Rarita-Schwinger Type operators on Cylinders
摘要：
本文定义了柱上的Rarita-Schwinger算子并构造了它们的基本解。进一步利用平移群得到了柱型Rarita-Schwinger型算子的基本解.进而给出了圆柱体的Borel-Pompeiu公式、柯西积分公式和柯西变换。此外，我们还证明了在这些圆柱上构造了一些共形不等价的旋量丛。在这种情况下，我们再次构造了Rarita-Schwinger算子及其基本解。最后，我们研究了柱上剩余的Rarita-Schwinger型算子。
英文摘要：
Here we define Rarita-Schwinger operators on cylinders and construct their fundamental solutions. Further the fundamental solutions to the cylindrical Rarita-Schwinger type operators are achieved by applying translation groups. In turn, a Borel-Pompeiu Formula, Cauchy Integral Formula and a Cauchy Transform are presented for the cylinders. Moreover we show a construction of a number of conformally inequivalent spinor bundles on these cylinders. Again we construct Rarita-Schwinger operators and their fundamental solutions in this setting. Finally we study the remaining Rarita-Schwinger type operators on cylinders.
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