Homogeneous and $\overline0$-homogeneous supermanifolds with retract $\mathbb{CP}^{1|4}_{kk20}$ when $k\ge 2$

M. A. Bashkin

Rybinsk State Aviation Technological Academy

Abstract: This paper contain the description of non-split even-homogeneous supermanifolds over the complex projective line whose retract corresponds to a holomorphic vector bundle of the signature $(k,k,2,0),$ where $k\ge 2$. We prove that there are no non-split homogeneous supermanifolds in this case. See [3] and [4] for more information about the complex supermanifolds theory.

Keywords: complex supermanifold, homogeneous complex supermanifold, retract, tangent sheaf.

UDC: 515.177

Received: 25.05.2009