Rarita-Schwinger Type Operators on Cylinders |
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Authors: | Junxia Li John Ryan Carmen Judith Vanegas |
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Institution: | 1. Department of Mathematics, University of Arkansas, Fayetteville, AR, 72701, USA 2. Departamento de Matemáticas, Universidad Simón Bolívar, Caracas, Venezuela
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Abstract: | 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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