Higher order fermionic and bosonic operators on cylinders and Hopf manifolds

TL;DR

This paper investigates higher order higher spin operators on cylinders and Hopf manifolds, focusing on their properties and kernel constructions within conformally flat geometries.

Contribution

It introduces new higher order higher spin operators on specific conformally flat manifolds and constructs their kernels, expanding the understanding of these operators in geometric analysis.

Findings

Defined higher order higher spin operators on cylinders and Hopf manifolds

Constructed explicit kernels for these operators on the manifolds

Extended the theory of higher spin operators to new geometric settings

Abstract

Higher order higher spin operators are generalizations of $kth$-powers of the Dirac operator. In this paper, we study higher order higher spin operators defined on some conformally flat manifolds, namely cylinders and Hopf manifolds. We will also construct the kernels of these operators on these manifolds.