The analogs of Riemann and Penrose tensors on supermanifolds

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

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。

The analogs of the Riemann tensor for exceptional structures on supermanifolds

H. Hertz called any manifold M with a given nonintegrable distribution {\it nonholonomic}. Vershik and Gershkovich stated and R. Montgomery proved that the space of germs of any nonholonomic distribution on M with an open and dense orbit of the diffeomorphism group is either (1) of codimension one or (2) an Engel distribution. No analog of this statement for supermanifolds is formulated yet, we only have some examples: our list (an analog of E.Cartan's classification) of simple Lie superalgebras of vector fields with polynomial coefficients and a particular (Weisfeiler) grading contains 16 ser…