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Generalized Helical Hypersurfaces Having Time-like Axis in Minkowski Spacetime
Universe ( IF 2.5 ) Pub Date : 2022-09-08 , DOI: 10.3390/universe8090469
Erhan Güler

In this paper, the generalized helical hypersurfaces x=x(u,v,w) with a time-like axis in Minkowski spacetime E14 are considered. The first and the second fundamental form matrices, the Gauss map, and the shape operator matrix of x are calculated. Moreover, the curvatures of the generalized helical hypersurface x are obtained by using the Cayley–Hamilton theorem. The umbilical conditions for the curvatures of x are given. Finally, the Laplace–Beltrami operator of the generalized helical hypersurface with a time-like axis is presented in E14.

中文翻译:

闵可夫斯基时空中具有类时轴的广义螺旋超曲面

在本文中,广义螺旋超曲面X=X(,v,w)在 Minkowski 时空中具有类时轴14被考虑。第一和第二基本形式矩阵、高斯图和形状算子矩阵X被计算。此外,广义螺旋超曲面的曲率X通过使用 Cayley-Hamilton 定理获得。曲率的脐带条件X给出。最后,具有类时轴的广义螺旋超曲面的拉普拉斯-贝尔特拉米算子在14.
更新日期:2022-09-09
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