论文标题
曲率遗传对称性在M训练平坦的空间上
Curvature inheritance symmetry on M-projectively flat spacetimes
论文作者
论文摘要
该论文旨在研究曲率遗传对称性，以平坦的空间为单位。结果表明，M-Projement flat时空中的曲率遗传对称性是一个共形运动。我们已经证明，当Spacetime接收曲率遗传对称性和沿矢量场$ξ$的曲率遗传对称性和同形运动的条件时，M-射击曲率张量遵循沿向量场$ξ$的对称性继承属性。此外，我们为M练习平坦的时空得出了一些结果，并在爱因斯坦田间方程遵循宇宙学术语的情况下获得了完美的流体，并接受了沿矢量场$ξ$的曲率遗传对称性。我们已经表明，具有宇宙学术语的M型扁平完美的液体时空服从爱因斯坦场方程，并接受沿矢量场$ξ$的曲率遗传对称性，或者满足状态真空状态方程。我们还表明，具有电磁场分布的能量动量张量的这种空间不承认一般相对性的任何曲率对称性。最后，已经展示了一个较平坦的时空的例子。
The paper aims to investigate curvature inheritance symmetry in M-projectively flat spacetimes. It is shown that the curvature inheritance symmetry in M-projectively flat spacetime is a conformal motion. We have proved that M- projective curvature tensor follows the symmetry inheritance property along a vector field $ξ$, when spacetime admits the conditions of both curvature inheritance symmetry and conformal motion or motion along the vector field $ξ$. Also, we have derived some results for M-projectively flat spacetime with perfect fluid following the Einstein field equations with a cosmological term and admitting the curvature inheritance symmetry along the vector field $ξ$. We have shown that an M-projectively flat perfect fluid spacetime obeying the Einstein field equations with a cosmological term and admitting the curvature inheritance symmetry along a vector field $ξ$ is either a vacuum or satisfies the vacuum-like equation of state. We have also shown that such spacetimes with the energy momentum tensor of an electromagnetic field distribution do not admit any curvature symmetry of general relativity. Finally, an example of M-projectively flat spacetime has been exhibited.
