近乎Kähler流形上的rita- schwinger场

IF 0.6 4区数学 Q3 MATHEMATICS

Differential Geometry and its Applications Pub Date : 2023-10-25 DOI:10.1016/j.difgeo.2023.102068

Soma Ohno , Takuma Tomihisa

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引用次数: 1

摘要

研究了6维紧致严格近似Kähler流形上的rita- schwinger场。为了研究它们，我们澄清了厄密连接和列维-奇维塔连接的一些微分算子之间的关系。结果表明，rita- schwinger场的空间与谐波3型空间重合。将同样的方法应用到变形理论中，我们也发现了消旋量的无穷小变形空间与拉普拉斯算子的某个特征空间与消旋量空间的直接和重合。

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Rarita-Schwinger fields on nearly Kähler manifolds

We study Rarita-Schwinger fields on 6-dimensional compact strict nearly Kähler manifolds. In order to investigate them, we clarify the relationship between some differential operators for the Hermitian connection and the Levi-Civita connection. As a result, we show that the space of Rarita-Schwinger fields coincides with the space of harmonic 3-forms. Applying the same technique to deformation theory, we also find that the space of infinitesimal deformations of Killing spinors coincides with the direct sum of a certain eigenspace of the Laplace operator and the space of Killing spinors.

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来源期刊

Differential Geometry and its Applications 数学-数学

CiteScore

1.00

自引率

20.00%

发文量

审稿时长

6-12 weeks

期刊介绍： Differential Geometry and its Applications publishes original research papers and survey papers in differential geometry and in all interdisciplinary areas in mathematics which use differential geometric methods and investigate geometrical structures. The following main areas are covered: differential equations on manifolds, global analysis, Lie groups, local and global differential geometry, the calculus of variations on manifolds, topology of manifolds, and mathematical physics.