Jacobi fields and the stability of minimal foliations of arbitrary codimension

TL;DR

This paper explores the stability of minimal foliations of any codimension, examining Jacobi fields, foliation-preserving vector fields, and their connections to Killing fields to understand geometric stability.

Contribution

It introduces new relationships between Jacobi fields and foliation-preserving vector fields, extending stability analysis to arbitrary codimension minimal foliations.

Findings

Established links between Jacobi fields and foliation-preserving vector fields.

Analyzed the role of Killing fields in the context of minimal foliations.

Provided criteria for stability of leaves in arbitrary codimension.

Abstract

In this article, we investigate the stability of leaves of minimal foliations of arbitrary codimension. We also study relations between Jacobi fields and vector fields which preserves a foliation and we use these results to Killing fields.