超流形上的辛标量曲率
Symplectic scalar curvature on supermanifolds
AI总结：
本文在 Fedosov 流形上的超流形中研究辛标量曲率，提出两族奇超 Fedosov 结构，并证明分次非对称联络可产生非平凡曲率，以环面为例给出具体计算。
摘要：
我们研究普通 Fedosov 流形上、结构层为微分形式层的超流形中的辛标量曲率概念。在这一纯几何背景下，我们引入两族奇超 Fedosov 结构：第一族非常一般，使用分次对称联络，导致奇辛标量曲率消失；第二族基于分次非对称联络，具有非平凡的奇辛标量曲率。作为第二类情形的一个简单例子，当底 Fedosov 流形为环面时，我们确定了该曲率。
英文摘要：
We study the notion of symplectic scalar curvature on the supermanifold over an ordinary Fedosov manifold whose structural sheaf is that of differential forms. In this purely geometric context, we introduce two families of odd super-Fedosov structures, the first one is very general and uses a graded symmetric connection, leading to a vanishing odd symplectic scalar curvature, while the second one is based on a graded non-symmetric connection and has a non-trivial odd symplectic scalar curvature. As a simple example of the second case, we determine that curvature when the base Fedosov manifold is the torus.
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