作为殆实-复超流形的Minkowski超空间与超弦
Minkowski superspaces and superstrings as almost real-complex supermanifolds
AI总结：
该研究提出殆实-复超流形概念以刻画Minkowski超空间与超弦，定义环切Nijenhuis张量并计算其结构，证明仅1|1维超弦的该张量为零且带切触结构，还证实复Grassmann代数所有实形式同构。
摘要：
1996至1997年，J. Bernstein指出，数学家研究的光滑或解析超流形是实的或（殆）复的，而Minkowski超空间是完全不同的对象。它们就是我们所说的殆实-复超流形，即带有一个不可积分布（切空间的子空间族）的实超流形，且每个子空间上都赋予了复结构。实超流形上的殆复结构可由偶算子或奇算子给出；当Nijenhuis张量的合适超化形式为零时，该结构是复的（并非始终为复）。在殆实-复超流形上，我们定义了“环切”版的Nijenhuis张量。我们针对Minkowski超空间和超弦计算了该张量。环切Nijenhuis张量的取值空间可分解为（通常是不可分解的）分量，其不可约组成部分与Riemann张量或Penrose张量的不可约组成部分相似。该Nijenhuis张量仅在超维数为1|1的超弦上恒为零，此外，这类超弦还带有切触结构。我们还证明，复Grassmann代数的所有实形式都是同构的，尽管它们是由明显不同的反对合所区分的。
英文摘要：
In 1996/7, J. Bernstein observed that smooth or analytic supermanifolds that mathematicians study are real or (almost) complex ones, while Minkowski superspaces are completely different objects. They are what we call almost real-complex supermanifolds, i.e., real supermanifolds with a non-integrable distribution, the collection of subspaces of the tangent space, and in every subspace a complex structure is given. An almost complex structure on a real supermanifold can be given by an even or odd operator; it is complex (without "always") if the suitable superization of the Nijenhuis tensor vanishes. On almost real-complex supermanifolds, we define the circumcised analog of the Nijenhuis tensor. We compute it for the Minkowski superspaces and superstrings. The space of values of the circumcised Nijenhuis tensor splits into (indecomposable, generally) components whose irreducible constituents are similar to those of Riemann or Penrose tensors. The Nijenhuis tensor vanishes identically only on superstrings of superdimension 1|1 and, besides, the superstring is endowed with a contact structure. We also prove that all real forms of complex Grassmann algebras are isomorphic although singled out by manifestly different anti-involutions.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
