Warped product rigidity

Chenxu He, Peter Petersen, William Wylie

Research output: Contribution to journalArticlepeer-review

7 Scopus citations


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].

Original languageEnglish (US)
Pages (from-to)135-170
Number of pages36
JournalAsian Journal of Mathematics
Issue number1
StatePublished - 2015


  • Hessian equations
  • Overdetermined linear system of differential equations
  • Ricci curvature
  • Warped product

ASJC Scopus subject areas

  • General Mathematics
  • Applied Mathematics


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