Differential Geometry

Vector fields on supermanifolds of $ \ Pi $ -symmetric flags

E. G. Vishnyakova

Tver State University, Tver

Abstract: We determine the Lie superalgebras of holomorphic vector fields on the complex supermanifolds of $\Pi$-symmetric flags, introduced by Yu.I. Manin (see [1]). The result is that, under certain restrictions, any vector field is fundamental for the natural action of the Lie superalgebra $\mathfrak q_n(\mathbb C)$. We use the results of the paper $[2]$, where the same problem for the $\Pi$-symmetric super-Grassmannians was considered.

Keywords: supermanifold of $\Pi$-symmetric flags, vector field, Lie superalgebra, super-Grassmannian, superbundle.

UDC: 517.54

Received: 17.09.2007
Revised: 16.10.2007

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