Rarita-Schwinger Type Operators on Spheres and Real Projective Space

TL;DR

This paper introduces Rarita-Schwinger type operators on spheres and real projective space, establishing their fundamental solutions, conformal invariance, integral formulas, and kernels, advancing the mathematical understanding of these operators in geometric contexts.

Contribution

It defines and analyzes Rarita-Schwinger type operators on spheres and real projective space, including their fundamental solutions, conformal invariance, and integral formulas, which is a novel extension in this field.

Findings

Constructed fundamental solutions for the operators.

Proved conformal invariance under Cayley transformation.

Derived integral formulas and kernels for the operators.

Abstract

In this paper we deal with Rarita-Schwinger type operators on spheres and real projective space. First we define the spherical Rarita-Schwinger type operators and construct their fundamental solutions. Then we establish that the projection operators appearing in the spherical Rarita-Schwinger type operators and the spherical Rarita-Schwinger type equations are conformally invariant under the Cayley transformation. Further, we obtain some basic integral formulas related to the spherical Rarita-Schwinger type operators. Second, we define the Rarita-Schwinger type operators on the real projective space and construct their kernels and Cauchy integral formulas.