What is the Bochner Technique and Where is it Applied

In the present article we consider the generalized Bochner technique that is a natural development of the classical Bochner technique. As an illustration, we prove some Liouville-type theorems for Killing and Killing–Yano tensors, as well as for projective and conformal mappings of complete Riemannian manifolds, using the $$L^{q}$$ -Liouville theorems for subharmonic and superharmonic functions.