General Mathematics, Vol. 5, No. 1 - 4, pp. 1127-134, 1995
Abstract: The present is an extended version of the talk given by the author on the occasion of the ``3rd International Workshop on Differential Geometry and its Applications and 1st German-Romanian Seminar on Geometry'' (Sibiu 1997). It is based on joint work with D.V.\ Alekseevsky, C.\ Devchand and U.\ Semmelmann, see \cite{A-C} and \cite{A-C-D-S}. A supermanifold $M$ is canonically associated to any pseudo Riemannian spin manifold $(M_0,g_0)$. Its structure sheaf is the sheaf of local sections of the exterior algebra $\wedge S$ over the spinor bundle $S \rightarrow M_0$. $M$ carries a $G$-structure ${\cal F}_G$ for a certain linear supergroup $G$ whose even part is the spinor group. $G$ is constructed using the coadjoint representation of a super extended Poincar\'e group. For any spinor field $s$ on $M_0$ there is a corresponding odd vector field $X_s$ on $M$. The twistor equation has the following supergeometric interpretation: $X_s$ is an infinitesimal automorphism of the G-structure ${\cal F}_G$ iff $S$ is a solution of the twistor equation.
Classification (MSC91):
Keywords:
Full text of the article:
[Next Article] [Contents of this Number] [Journals Homepage]