On differential operators generated by geometric structures

TL;DR

This paper generalizes the concepts of gradient and Laplace operator to manifolds with various geometric structures, exploring their fundamental properties.

Contribution

It introduces a unified framework for defining differential operators on manifolds with diverse geometric structures, extending classical notions.

Findings

Defined generalized gradient and Laplace operators

Established fundamental properties of these operators

Unified approach applicable to various geometric structures

Abstract

We extend to manifolds endowed with a general geometric structure, the classical notions of gradient as well as Laplace operator, and provide some of their natural properties.