# Matsushima-Shimura theorem

From Diffgeom

Template:Metric rigidity theorem

## Statement

Let be an irreducible compact quotient of a polydisc. Then:

- As a corollary, is locally rigid as a complex manifold

## Relation with other results

### Calabi-Vesentini theorem

This draws the same conclusions from slightly more relaxed hypotheses.

`Further information: Calabi-Vesentini theorem`