k-Dirac operator and the Cartan-Kahler theorem for weighted differential operators

TL;DR

This paper explores the k-Dirac operator, a geometric differential operator of parabolic type, establishing initial conditions and adapting exterior differential systems theory to weighted differential operators.

Contribution

It introduces initial conditions for the k-Dirac operator and adapts exterior differential systems theory to weighted differential operators.

Findings

Set of initial conditions for the k-Dirac operator

Adaptation of exterior differential systems to weighted operators

Theoretical framework for parabolic geometric operators

Abstract

The k-Dirac operator is a differential operator which is natural to geometric structure of a parabolic type. We will give a set of initial conditions for this operator. In the proof of the claim we will need to adapt some parts from the theory of exterior differential systems to the setting of weighted differential operators.