Relations between Killing, Global Jacobi and Solenoidal Vector Fields

TL;DR

This paper explores the relationships between Killing, global Jacobi, and solenoidal vector fields on manifolds, highlighting differences between compact and noncompact cases due to integration properties.

Contribution

It provides a comparative analysis of these vector fields on different types of manifolds, emphasizing the impact of compactness on their relationships.

Findings

Relationships vary significantly between compact and noncompact manifolds.

Integration over compact manifolds influences the properties of these vector fields.

The study clarifies how manifold topology affects vector field characteristics.

Abstract

In this article we investigate the relations between three kinds of vector fields with close connection to each other. A compact orientable manifold enables us to integrate over it, which is very different from noncompact manifolds, and this gives difference of those relationships between on compact and noncompact manifolds.