Geometry of 1-parameter subgroups of Lie groups

The project aims to contribute to the study of curves in homogeneous spaces (the spaces with a very large amount of symmetry). We consider a class of naturally defined distinguished curves, the 1-parameter subgroups of a metric Lie group, and determine their
curvatures. The research question which we will address in this study is the classification
of the so-called homogeneous circles, the curves whose (first) curvature is nonzero, but all
the higher curvatures vanish. There is a substantial amount of research on the circles in
homogeneous spaces. The project will start with understanding the known methods,
techniques and results. The objective will be to classify homogeneous circles in lowdimensional and in some other classes of metric Lie groups (like eg almost abelian). The
educational component will also involve getting working experience in the relevant
software packages (Maple, Latex, etc)

Soprom Meng

La Trobe University

Soprom is a third-year undergraduate student at La Trobe university. He is undertaking a Bachelor of Science majoring in Mathematics and minoring in Statistics. The main reason that he decided to peruse this bachelor’s degree because he has been good at math since he was at primary school, and he is very keen to utilize mathematical knowledge to solve the real problems.

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