Tohoku Mathematical Journal
- Tohoku Math. J. (2)
- Volume 69, Number 4 (2017), 621-635.
Minimal timelike surfaces in a certain homogeneous Lorentzian 3-manifold
The 2-parameter family of certain homogeneous Lorentzian 3-manifolds which includes Minkowski 3-space, de Sitter 3-space, and Minkowski motion group is considered. Each homogeneous Lorentzian 3-manifold in the 2-parameter family has a solvable Lie group structure with left invariant metric. A generalized integral representation formula which is the unification of representation formulas for minimal timelike surfaces in those homogeneous Lorentzian 3-manifolds is obtained. The normal Gauß map of minimal timelike surfaces in those homogeneous Lorentzian 3-manifolds and its harmonicity are discussed.
Tohoku Math. J. (2), Volume 69, Number 4 (2017), 621-635.
First available in Project Euclid: 2 December 2017
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 53A10: Minimal surfaces, surfaces with prescribed mean curvature [See also 49Q05, 49Q10, 53C42]
Secondary: 53C30: Homogeneous manifolds [See also 14M15, 14M17, 32M10, 57T15] 53C42: Immersions (minimal, prescribed curvature, tight, etc.) [See also 49Q05, 49Q10, 53A10, 57R40, 57R42] 53C50: Lorentz manifolds, manifolds with indefinite metrics
Lee, Sungwook. Minimal timelike surfaces in a certain homogeneous Lorentzian 3-manifold. Tohoku Math. J. (2) 69 (2017), no. 4, 621--635. doi:10.2748/tmj/1512183633. https://projecteuclid.org/euclid.tmj/1512183633