Einstein metrics induced by natural Riemann extensions
Einstein metrics with positive scalar curvature have many applications and their existence (or nonexistence) on various types of manifolds was studied in many papers. In the present paper, the natural Riemann extension \((T^*M,\bar g)\) of a surface \(M\) is considered. It is a pseudo-Riemannian manifold of neutral signature and its non-degenerate hypersurfaces are Lorentzian manifolds. Families of such hypersurfaces are constructed which are Einstein with positive scalar curvature.
scientific article; zbMATH DE number 6835284
scientific article