辛Killing旋量
Symplectic Killing spinors
摘要：
设$(M,ω)$是一个具有亚辛结构（黎曼自旋结构的辛模拟）和无挠辛联络的辛流形，这种结构的辛Killing旋量场是满足一阶偏微分方程的辛旋量丛的截面，这是本文的主要内容。本文导出了辛Killing旋量场满足的一个必要条件。这个条件的优点在于它是由零阶算子表示的。这个条件有助于我们在实质上计算标准辛向量空间和具有圆度量的体积形式的圆球$S^2$的辛Killing旋量场。
英文摘要：
Let $(M,ω)$ be a symplectic manifold admitting a metaplectic structure (a symplectic analogue of the Riemannian spin structure) and a torsion-free symplectic connection $\nabla.$ Symplectic Killing spinor fields for this structure are sections of the symplectic spinor bundle satisfying a certain first order partial differential equation and they are the main topic of this paper. We derive a necessary condition satisfied by a symplectic Killing spinor field. The advantage of this condition consists in the fact that it is expressed by a zeroth order operator. This condition helps us substantionally to compute the symplectic Killing spinor fields for the standard symplectic vector spaces and the round sphere $S^2$ equipped with the volume form of the round metric.
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