论文标题
超质量曲率上的超稳态曲率
Symplectic scalar curvature on supermanifolds
论文作者
论文摘要
我们研究了一个普通的Fedosov歧管上的超模型标量曲率的概念，该曲线的结构捆扎是差异形式的概念。在这种纯粹的几何环境中，我们介绍了两个奇怪的超级富裕结构的家族，第一个是非常通用的，并使用了渐变的对称连接，从而导致奇数奇异的标量曲率消失，而第二个则基于渐变的非对称连接，并且具有非奇特的奇异标量曲率。作为第二种情况的一个简单示例，我们确定基本Fedosov歧管是圆环时的曲率。
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.
