The Bjorling problem for timelike minimal surfaces in R-1(4)

作者：Dussan M P^*; Franco Filho A P; Magid M

来源：Annali di Matematica Pura ed Applicata, 2017, 196(4): 1231-1249.

DOI：10.1007/s10231-016-0614-3

• Timelike surfaces
• Bjorling problem
• Lorentz-Minkowski space
• Symmetry principles

In this paper, we extend and solve the Bjorling problem for timelike surfaces in the ambient space R-1(4) . To do this, we define a Gauss map ideally suited to this setting using the split-complex variable and then we obtain a Weierstrass representation formula. We use this to construct new examples and give applications. In particular, we obtain one-parameter families of timelike surfaces in R-1(4) which are solutions of the timelike Bjorling problem. In addition, we establish symmetry principles for the class of minimal timelike surfaces in R-1(4) .

• 出版日期2017-8