There are different notions of "rigidity" (local rigidity, global rigidity, infinitesimal rigidity, étale rigidity and strong rigidity) and many examples for each of them.

This topic is discussed in the paper by I. Bauer and F. Catanese On rigid compact complex surfaces and manifolds, you can have a look at it for more details and references to the literature.

There are several different notions of "rigidity" (local rigidity, global rigidity, infinitesimal rigidity, étale rigidity and strong rigidity) and it is possible to provide examples for each of them.

This topic is discussed in the paper by I. Bauer and F. Catanese On rigid compact complex surfaces and manifolds, you can have a look at it for more details and references to the literature.