We give a number of new examples of timelike minimal surfaces in the Lorentz-Minkowski space. Our method consists of solving the Björling problem by prescribing a circle or a helix as the core curve $\alpha$ and rotating with constant angular speed the unit normal vector field in the normal plane to $\alpha$. As particular cases, we exhibit new examples of timelike minimal surfaces invariant by a uniparametric group of helicoidal motions.
Timelike minimal surface, Björling problem, circle, helix
KAYA, SEHER and LOPEZ, RAFAEL
"Solutions of the Björling problem for timelike surfaces in the Lorentz-Minkowski space,"
Turkish Journal of Mathematics: Vol. 42:
5, Article 9.
Available at: https://journals.tubitak.gov.tr/math/vol42/iss5/9