论文标题
超曼佛（Supermanifolds）上的奇数连接：存在和与仿射连接的关系
Odd Connections on Supermanifolds: Existence and relation with Affine Connections
论文作者
论文摘要
研究了对超曼属的奇数准连接的概念，该概念是一种呈现非零Grassmann Parity的仿射连接的概念。他们的扭转和曲率是定义的，但是，通常它们不是张量。在本文中称为奇数连接的特殊类别的特殊连接，具有扭转和曲率张量。结构的一部分是超人的切线束的奇怪涉及，这使得对接收奇数连接的超级曼尼属造成了巨大的限制。特别是，它们必须具有相等数量的偶数和奇数。在其他结果中，我们表明，通过仿射连接和切线束的奇数内态性，定义了一个奇数连接，直至类型$（1,2）$的奇数张量字段。因此，奇数连接和仿射连接的理论并不是完全独立的理论。作为与物理相关的示例，显示出$ n = 1 $ super-minkowski SpaceTime承认自然的奇数连接。
The notion of an odd quasi-connection on a supermanifold, which is loosely an affine connection that carries non-zero Grassmann parity, is examined. Their torsion and curvature are defined, however, in general, they are not tensors. A special class of such generalised connections, referred to as odd connections in this paper, have torsion and curvature tensors. Part of the structure is an odd involution of the tangent bundle of the supermanifold and this puts drastic restrictions on the supermanifolds that admit odd connections. In particular, they must have equal number of even and odd dimensions. Amongst other results, we show that an odd connection is defined, up to an odd tensor field of type $(1,2)$, by an affine connection and an odd endomorphism of the tangent bundle. Thus, the theory of odd connections and affine connections are not completely separate theories. As an example relevant to physics, it is shown that $N= 1$ super-Minkowski spacetime admits a natural odd connection.
