Rigid representations of Kählerian fundamental groups
It is known that cocompact lattices in a semisimple Lie group have no deformations, provided the group has no local three-dimensional factors. This paper is devoted to the study of the local rigidity in the context of locally symmetric manifolds. More precisely, the main purpose is to prove the following Theorem: Suppose that P is a flat principal \(G_{{\mathbb{R}}}\)-bundle over a compact Kähler manifold M with vol(P)\(\neq 0\), and assume that \(G_{{\mathbb{R}}}/K\) is not of the form U(n,1)/U(n)\(\times U(1)\) or \(SO(2n+1,2)/S(O(2n+1)\times O(2)).\) Then the monodromy homomorphism of the fundamental group of M into \(G_{{\mathbb{R}}}\) is locally rigid as a homomorphism into the complexification of \(G_{{\mathbb{R}}}\). Here \(G_{{\mathbb{R}}}\) is a simple real algebraic group acting by isometries on the irreducible bounded symmetric domain \(G_{{\mathbb{R}}}/K\).
scientific article; zbMATH DE number 4209027