Stability of Geodesics on Three-Dimensional Lie Groups

In Riemannian geometry, geodesics play the same role as a straight line in plane geometry: it is the “straightest” and the shortest distance between two points. Despite its important definition, the methods to solve for an geodesics involve solving a system of second order ODEs which are non-linear in the first derivatives, and hence most likely difficult to solve. The aim of this project is to fully understand the stability of geodesics on metric Lie groups in the first non-trivial dimension, n = 3.

An Ky Duy Nguyen

La Trobe University

An Ky Duy (Kyan) Nguyen is a third-year Mathematics major student at La Trobe University. His research interest is mainly pure mathematics, with focuses on analysis, algebra, geometry, number theory and how they all are interconnected. To him Mathematics has been a lifelong passion, yet the more he learns, the broader Maths seems to become. In his free time, he enjoys going to the gym, and reading into the history of Maths, other mathematicians and famous problems.

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