Rarita-Schwinger Type operators on Cylinders

TL;DR

This paper introduces Rarita-Schwinger operators on cylinders, constructs their fundamental solutions, and develops integral formulas and spinor bundle structures, advancing the mathematical framework for these operators in cylindrical geometries.

Contribution

It defines Rarita-Schwinger operators on cylinders, constructs their fundamental solutions, and develops integral formulas and spinor bundle structures, which are novel contributions in this area.

Findings

Fundamental solutions for cylindrical Rarita-Schwinger operators are constructed.

Integral formulas like Borel-Pompeiu and Cauchy are established for cylinders.

Construction of conformally inequivalent spinor bundles on cylinders is achieved.

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.