Warped product rigidity

Chenxu He, Peter Petersen, William Wylie

Research output: Contribution to journalArticle

3 Scopus citations

Abstract

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
Volume19
Issue number1
DOIs
StatePublished - 2015

Keywords

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

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

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