Symmetries and pseudo-Riemannian manifolds (Q1107142)

Analogues of the classical Bochner-Yano and Hopf-Bochner theorems for closed Riemannian manifolds are investigated in the case of noncompact pseudo-Riemannian spaces. It turns out that the hyperbolic versions of these theorems are much weaker, i.e. the relationship between curvature, topology and symmetry (the Killing vector fields) is not so strong as in the elliptic case. Possible applications to Kaluza-Klein theory and general relativity are briefly mentioned.