Timelike surfaces with zero mean curvature in Minkowski 4-space

Abstract

On any timelike surface with zero mean curvature in the four-dimensional Minkowski space we introduce special geometric (canonical) parameters and prove that the Gauss curvature and the normal curvature of the surface satisfy a system of two natural partial differential equations. Conversely, any two solutions to this system determine a unique (up to a motion) timelike surface with zero mean curvature so that the given parameters are canonical. We find all timelike surfaces with zero mean curvature in the class of rotational surfaces of Moore type. These examples give rise to a one-parameter family of solutions to the system of natural partial differential equations describing timelike surfaces with zero mean curvature.

15 pages

References in corpus (5)

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Cited by in corpus (6)

• Minimal Lorentz Surfaces in Pseudo-Euclidean 4-Space with Neutral Metric
• Explicit Solving of the System of Natural PDE's of Minimal Space-like Surfaces in Minkowski Space-time
• Canonical coordinates on minimal time-like surfaces in the n-dimensional Minkowski space
• Fundamental Theorems for Timelike Surfaces in the Minkowski 4-Space
• On rotational surfaces with zero mean curvature in the pseudo-Euclidean space ${\mathbb{E}}_2^4$
• Canonical Coordinates and Natural Equation for Lorentz Surfaces in ${\mathbb{R}}_1^3$