Title

Minimal Timelike Surfaces In a Certain Homogeneous Lorentzian 3-Manifold

Document Type

Article

Publication Date

12-1-2017

Department

Mathematics

School

Mathematics and Natural Sciences

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 GauB map of minimal timelike surfaces in those homogeneous Lorentzian 3-manifolds and its harmonicity are discussed.

Publication Title

Tohoku Mathematical Journal

Volume

69

Issue

4

First Page

621

Last Page

635

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