A note on proper curvature symmetry in general cylindrically symmetric four-dimensional Lorentzian manifolds

作者：Shabbir Ghulam^*; Ramzan M; Kara A H

来源：International Journal of Geometric Methods in Modern Physics, 2018, 15(6): 1850105.

DOI：10.1142/S0219887818501050

• Rank of the 6 x 6 Riemann matrix
• proper curvature symmetry
• direct integration technique

We considered the most general form of non-static cylindrically symmetric space-times for studying proper curvature symmetry by using the rank of the 6 x 6 Riemann matrix and direct integration techniques. Studying proper curvature symmetry in each case of the above space-times, we show that when the above space-times admit proper curvature symmetry, they form an infinite dimensional vector space. It is important to note that here we also find the case when the rank of the 6 x 6 Riemann matrix is one and no covariantly constant vector fields exist.

• 出版日期2018-6