The aim of the present paper is to study the theory of general relativity in a Lorentzian Kähler space. In this paper, we have considered the Lorentzian complex space form with constant sectional curvature and proved that a Lorentzian complex space form satisfying Einstein’s field equation is a Ricci semi-symmetric space and the energy–momentum tensor is covariant constant. Such space reduces to a flat space for a purely electromagnetic distribution. The existence of the Killing vector field and conformal Killing vector field has been discussed and proved that the cosmological term is proportional to sectional curvature. Further, it is shown that the perfect fluid in a Lorentzian complex space form satisfying Einstein’s field equation does not admit heat flux.

中文翻译：

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洛伦兹复杂空间形式

本文的目的是研究LorentzianKähler空间中的广义相对论。在本文中，我们考虑了具有恒定截面曲率的洛伦兹复杂空间形式，并证明满足爱因斯坦场方程的洛伦兹复杂空间形式是Ricci半对称空间，并且能量动量张量是协变常数。该空间减小为用于纯电磁分布的平坦空间。讨论了Killing向量场和保形Killing向量场的存在，并证明宇宙学项与截面曲率成正比。此外，还表明，在满足爱因斯坦场方程的洛伦兹复杂空间形式中的理想流体不允许热通量。