An elliptic proof of the splitting theorems from Lorentzian geometry

We initiate the development of a theory of the negative homogeneity p p -d’Alembert operator in the smooth setting. We relate it to a Bochner-Ohta identity of homogeneity 2 p − 2 > 0 2p-2>0 . We identify conditions under which the unexpected ellipticity of this operator turns out to be uniform. We exploit this to give a new proof of the Eschenburg, Galloway and Newman splitting theorems from Lorentzian geometry, which allows us bring them into a framework closer to the Cheeger-Gromoll splitting theorem from Riemannian geometry.