Gauduchon-Tod structures, Sim holonomy and De Sitter supergravity
Gauduchon-Tod structures, Sim holonomy and De Sitter supergravity
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高杜雄-托德结构、Sim 完整性和德西特超引力
DOI：
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发表时间：
2009
期刊：
影响因子：
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通讯作者：
W. Sabra
中科院分区：
文献类型：
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作者：
J. Grover;J. Gutowski;C. Herdeiro;P. Meessen;A. Palomo;W. Sabra
利用旋量几何方法，研究了含有Killing旋量的五维De Sitter超引力解.它表明，''零'的解决方案被定义在一个参数家庭的三维约束Einstein-Weyl空间称为Gauduchon-Tod结构。它们允许测地线、无膨胀、无扭曲和无剪切的零向量场，因此是一种特殊类型的孔特几何。当Gauduchon-Tod结构简化为3-球面时，零向量变得循环，因此完整性包含在Sim（3）中，Sim（3）是洛伦兹群SO（4，1）的最大真子群。对于这些几何体，从曲率构建的所有标量不变量都是常数。明确的例子进行了讨论。
Solutions of five-dimensional De Sitter supergravity admitting Killing spinors are considered, using spinorial geometry techniques. It is shown that the ``null' solutions are defined in terms of a one parameter family of 3-dimensional constrained Einstein-Weyl spaces called Gauduchon-Tod structures. They admit a geodesic, expansion-free, twist-free and shear-free null vector field and therefore are a particular type of Kundt geometry. When the Gauduchon-Tod structure reduces to the 3-sphere, the null vector becomes recurrent, and therefore the holonomy is contained in Sim(3), the maximal proper subgroup of the Lorentz group SO(4,1). For these geometries, all scalar invariants built from the curvature are constant. Explicit examples are discussed.