**志賀 啓成**

**99.6.1, 数学教室談話会**

Let
be a complex hyperbolic manifold of divergence type
and *M* a
complex manifold which may not be compact nor complex hyperbolic. In
this talk, we shall consider the (strong) rigidity for non-constant
holomorphic maps of *N* to *M*. Generally, the rigidity does not hold.
Hence, we shall consider sufficient conditions for the manifold *M* to
have the rigidity. As an application, we shall establish a
finiteness theorem for holomorphic maps of *N* to *M* if
is
finitely generated and if *M* is compact.

Also, we shall construct examples of the manifold *M* with the
rigidity for holomorphic mappings of *N* and consider related topics.