Martha P. Dussan -- Timelike surfaces in the De Sitter space via the complex numbers
Author information
- Martha P. Dussan
- University of Sao Paulo - Brazil
Abstract:
We present a method of describing all timelike surfaces in \(\mathbb S^3_1(1)\) using null coordinates and complex variable. We use stereographic projection to identify necessary and sufficient conditions for lifting our timelike surfaces in \(\mathbb S^3_1(1)\) into a special complex quadric of the complex projective space and then we study that surfaces. In particular we introduce a new class of complex functions, called quasi-holomorphic, that contains the holomorphic and anti-holomorphic functions. Next, we obtain a remarkable correspondence between timelike minimal surfaces in \(\mathbb S^3_1(1)\) and pairs of quasi-holomorphic functions.
This work is joint with Prof. A.P. Franco-Filho (IME-USP) and M. Magid (Wellesley College).