Minimal unit vector fields on oscillator groups

TL;DR

This paper investigates minimal left-invariant unit vector fields on oscillator groups and their connection to harmonic maps, showing that uniform structure constants lead to all such vector fields being minimal.

Contribution

It characterizes minimal vector fields on oscillator groups and links them to harmonic maps, especially under uniform structure constants.

Findings

All unit left invariant vector fields defining harmonic maps are minimal when structure constants are equal.

The paper establishes a relationship between harmonic maps and minimal vector fields on oscillator groups.

Uniform structure constants imply all harmonic map-defining vector fields are minimal.

Abstract

In this paper, we treat minimal left-invariant unit vector fields on oscillator group and their relations with the ones that define a harmonic map. Particularly, if all structure constants of the oscillator group are equal to each other, then all unit left invariant vector fields that define a harmonic map into the unit tangent bundle with Sasaki metric are minimal.