Canonical Weierstrass Representation of Minimal Lorentz Surfaces in Pseudo-Euclidean 4-Space with Neutral Metric

Explore the canonical Weierstrass representation of minimal Lorentz surfaces in pseudo-Euclidean 4-space with neutral metric in this 42-minute lecture. Delve into the properties of minimal Lorentz surfaces of general type, including their special isothermal parameters and the system of natural partial differential equations governing their Gauss and normal curvatures. Learn how to obtain a Weierstrass representation for these surfaces using canonical parameters, and discover how to describe them in terms of four real functions. Examine the explicit solution to the system of equations and study examples of minimal Lorentz surfaces of general type in E4_2 parametrized by canonical parameters. Gain insights into advanced topics in differential geometry and minimal surface theory as presented by a researcher from the Institute of Mathematics and Informatics at the Bulgarian Academy of Sciences.

Velichka Milousheva, Institute of Mathematics and Informatics, Bulgarian Academy of Sciences