Asian Journal of Mathematics
Volume 19 (2015)
Warped product rigidity
Pages: 135 – 170
In this paper we study the space of solutions to an overdetermined linear system involving the Hessian of functions. We show that if the solution space has dimension greater than one, then the underlying manifold has a very rigid warped product structure. We obtain a uniqueness result for prescribing the Ricci curvature of a warped product manifold over a fixed base. As an application, this warped product structure will be used to study warped product Einstein structures in [HPW4].
warped product, Ricci curvature, Hessian equations, overdetermined linear system of differential equations
2010 Mathematics Subject Classification