On vanishing theorems and rigidity of locally symmetric manifolds (Q5937272)

Rigidity results of locally symmetric spaces have been intensively investigated by many people recently. One approach is to use a Bochner formula to derive some vanishing results and then rigidity results, and the Bochner formula can in turn be derived from an integral equality involving a 4-tensor. In this paper, the author makes use of different choices of the tensor in such an integral equality to give a uniform approach to prove many new and well-known vanishing and rigidity results, for example, the geometric superrigidity result of cocompact lattices, metric rigidity of locally Hermitian symmetric spaces, and vanishing of bundle valued harmonic forms which is not covered by the usual group representational approach.