Non-split supermanifolds associated with the cotangent bundle

Here, I study the problem of classification non-split supermanifolds having as retract split supermanifold $(M,\Omega)$, where $\Omega$ is sheaf holomorphic forms on a given complex manifold $M$ dimension $> 1$. propose general construction associating with any $d$-closed $(1,1)$-form $\omega$ $(M,\Omega)$ which whenever Dolbeault class non-zero. In particular, this gives non-empty family for flag $M\ne \mathbb{CP}^1$. case an irreducible compact Hermitian symmetric space, get complete $(M,\Omega)$. For each these supermanifolds, 0- and 1-cohomology values in tangent are calculated. As example, $\Pi$-symmetric super-Grassmannians introduced by Yu. Manin.