Solutions of the Bjorling problem for timelike surfaces in the Lorentz-Minkowski space

Kaya S., Lopez R.

TURKISH JOURNAL OF MATHEMATICS, vol.42, no.5, pp.2186-2201, 2018 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 42 Issue: 5
  • Publication Date: 2018
  • Doi Number: 10.3906/mat-1801-93
  • Journal Name: TURKISH JOURNAL OF MATHEMATICS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, TR DİZİN (ULAKBİM)
  • Page Numbers: pp.2186-2201
  • Keywords: Timelike minimal surface, Bjorling problem, circle, helix, MAXIMAL SURFACES, MINIMAL-SURFACES, GEOMETRY
  • Ankara University Affiliated: Yes

Abstract

We give a number of new examples of timelike minimal surfaces in the Lorentz-Minkowski space. Our method consists of solving the Bjorling problem by prescribing a circle or a helix as the core curve a 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.