Tohoku Mathematical Journal

Minimal timelike surfaces in a certain homogeneous Lorentzian 3-manifold

Sungwook Lee

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Abstract

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.

Article information

Source
Tohoku Math. J. (2), Volume 69, Number 4 (2017), 621-635.

Dates
First available in Project Euclid: 2 December 2017

Permanent link to this document
https://projecteuclid.org/euclid.tmj/1512183633

Digital Object Identifier
doi:10.2748/tmj/1512183633

Mathematical Reviews number (MathSciNet)
MR3732891

Zentralblatt MATH identifier
1384.53054

Subjects
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

Keywords
de Sitter space harmonic map homogeneous manifold Lorentz surface Lorentzian manifold Minkowski space minimal surface solvable Lie group spacetime timelike surface

Citation

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


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