On invariant properties of natural differential operators associated to geometric structures on $\mathbb{R}^n$

TL;DR

This paper develops a general framework to analyze invariant properties of gradient-like and Laplace-like differential operators linked to diverse geometric structures on , including Euclidean, Minkowski, pseudo-Euclidean, and symplectic geometries.

Contribution

It introduces a unified approach to study invariance of differential operators across multiple geometric structures on .

Findings

Framework applies to Euclidean, Minkowski, pseudo-Euclidean, and symplectic structures.

Identifies invariant properties of gradient-like and Laplace-like operators.

Enables systematic analysis of differential operators in various geometric contexts.

Abstract

We provide a general framework to study invariant properties of various gradient-like and Laplace-like differential operators naturally associated to geometric structures on $\mathbb{R}^n$, which encompass Euclidean, Minkowski, pseudo-Euclidean and symplectic structures.