（伪）Kähler-Einstein几何
(Pseudo-)Kähler-Einstein geometries
摘要：
具有宇宙学常数的真空爱因斯坦场方程的解，如de Sitter空间和反de Sitter空间，是不同宇宙学和理论发展的基础。众所周知，复杂的结构允许这种类型的度量。最著名的例子是赋予Fubini-Study度量的复射影空间。在这项工作中，我们进行了系统的研究爱因斯坦复杂的几何来自对数凯勒潜力。根据不同的贡献，这种对数项的论点，我们将区分直接，倒置和混合坐标。它们与度量的签名直接相关，并确定可以定义几何的复空间的最大域。
英文摘要：
Solutions to vacuum Einstein field equations with cosmological constant, such as the de Sitter space and the anti-de Sitter space, are basic in different cosmological and theoretical developments. It is also well known that complex structures admit metrics of this type. The most famous example is the complex projective space endowed with the Fubini-Study metric. In this work, we perform a systematic study of Einstein complex geometries derived from a logarithmic Kähler potential. Depending on the different contribution to the argument of such logarithmic term, we shall distinguish among direct, inverted and hybrid coordinates. They are directly related to the signature of the metric and determine the maximum domain of the complex space where the geometry can be defined.
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