Rotational hypersurfaces in Lorentz-Minkowski 4-space

Abstract

In this study, we study rotational hypersurfaces in 4-dimensional Lorentz-Minkowski space. We find the rotational hypersurfaces about spacelike axis according to Gaussian and mean curvatures in $E_{1}^{4}$ and give some results with the aid of the Gaussian and mean curvatures. After that, we deal with the Gauss map of rotational hypersurface about spacelike axis by obtaining the Gaussian and mean curvatures. We obtain the second and third Laplace-Beltrami operators on rotational hypersurface about spacelike axis in $E_{1}^{4}$. Also, we give these characterizations for rotational hypersurfaces about timelike and lightlike axes, too.

Keywords

• Rotational hypersurface
• Gauss map
• Second Laplace-Beltrami operator
• Third Laplace-Beltrami operator

References

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