Anna Kervison has just finished her final year of a dual degree (BSc/BE) majoring in mathematics and chemical engineering at UQ. She is will be commencing Honors in mathematics this year under the supervision of Dr Artem Pulemotov in the field of differential geometry. During the first half of this year, she completed an exchange semester at UC Berkeley, where she studied complex analysis, ordinary differential equations and recursion theory. Her mathematical interests lie in functional analysis and geometric analysis, with her research this summer and next year examining Riemannian geometry and Ricci curvature.
The Ricci Curvature Of Rotationally Symmetric Metrics
A manifold is a topological space that locally resembles Euclidean space. Its shape is defined by the Riemannian metric. The Ricci curvature is one of the measures of the curvature of the manifold; however, it is a complicated expression that requires additional simplifications to become manageable. A useful property of rotationally invariant Riemannian metrics is that they are conformal to a flat metric, with the consequence that the formula for the Ricci curvature simplifies significantly. The project aims to show how this allows one to reduce the prescribed Ricci curvature problem to an ordinary differential equation.