Timelike rotational hypersurfaces with timelike axis in Minkowski four-space

Abstract

We introduce the timelike rotational hypersurfaces $\textbf{x}$ with timelike axis in Minkowski 4-space $\mathbb{E}_1^{4}$. We obtain the equations for the curvatures of the hypersurface. Moreover, we present a theorem for the rotational hypersurfaces with timelike axis supplying $\Delta\textbf{x}=\mathcal{T}\textbf{x}$, where $\mathcal{T}$ is a 4x4 real matrix.

Keywords

• Rotational hypersurface
• timelike axis
• Laplace-Beltrami operator
• curvature
• Minkowski 4-space

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