关于辛扭量复形的椭圆性
On the ellipticity of symplectic twistor complexes
摘要：
对于具有亚辛结构的Fedosov流形（具有辛无挠仿射联络$\nabla$的辛流形），我们将研究作用在该流形上某些丛的截面上的两列一阶微分算子.这些算子是黎曼自旋几何中扭量算子的辛类似物。因此我们称上述序列为辛扭量序列。如果连接$\nabla$是Ricci型，则这些序列是复合体。我们将证明这些复形的所谓截断部分是椭圆形的。这为未来的分析研究奠定了背景。
英文摘要：
For a Fedosov manifold (symplectic manifold equipped with a symplectic torsion-free affine connection $\nabla$) admitting a metaplectic structure, we shall investigate two sequences of first order differential operators acting on sections of certain bundles over this manifold. The operators are symplectic analogues of the twistor operators known from Riemannian spin geometry. Therefore we call the mentioned sequences symplectic twistor sequences. These sequences are complexes if the connection $\nabla$ is of Ricci type. We shall prove that the so called truncated parts of these complexes are elliptic. This establishes a background for a future analytic study.
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