Growth conditions, Riemannian completeness and Lorentzian causality (Q764518)

This elegant paper presents a study of pointwise conformal transformations of certain Riemannian metrics on the fibres and growth conditions on the corresponding conformal factors. As it is known, a conformal transformation may not always preserve the completeness of the metric. Using the growth of the conformal factor, the authors find necessary and sufficient conditions for a conformally transformed Riemannian metric to be complete. An application is found in terms of relations between the completeness of Riemannian metrics, growth conditions on conformal factors and the Cauchy hypersurface condition on the fibres of a standard stationary spacetime.