Homogeneous supermanifolds associated with complex projective space. II

The study of homogeneous and evenly homogeneous complex supermanifolds of dimension $n|m$ whose reduction is the complex projective space $\mathbb {CP}^n$ is continued. All non-split supermanifolds of this type with retract admitting the full projective group as group of automorphisms are classified. The cohomology with values in the tangent sheaf is calculated for homogeneous supermanifolds satisfying the above-mentioned conditions.