A method for the resolution of the Jacobi equation Y''+RY = 0 on the manifold Sp(2)/SU(2)

TL;DR

This paper introduces a method to solve the Jacobi equation on the manifold Sp(2)/SU(2), enabling the calculation of geometric quantities like areas and volumes of geodesic spheres and balls.

Contribution

It presents a novel approach for solving the Jacobi equation specifically on the manifold Sp(2)/SU(2), facilitating geometric measurements.

Findings

Method successfully solves the Jacobi equation on Sp(2)/SU(2)

Allows computation of areas and volumes of geodesic spheres and balls

Provides new tools for geometric analysis on this manifold

Abstract

In this paper a method for the resolution of the differential equation of the Jacobi vector fields in the manifold V1 = Sp(2)/SU(2) is exposed. These results are applied to determine areas and volumes of geodesic spheres and balls.