Rigidity of homogeneous gradient soliton metrics and related equations

Peter Petersen, William Wylie

Research output: Contribution to journalArticlepeer-review

4 Scopus citations


We prove structure results for homogeneous spaces that support a non-constant solution to two general classes of equations involving the Hessian of a function and an invariant 2-tensor. We also consider trace-free versions of these systems. Our results generalize earlier rigidity results for gradient Ricci solitons and warped product Einstein metrics. In particular, our results apply to homogeneous gradient solitons of any invariant curvature flow and give a new structure result for homogeneous conformally Einstein metrics.

Original languageEnglish (US)
Article number101929
JournalDifferential Geometry and its Application
StatePublished - Oct 2022


  • Gradient soliton
  • Hessian
  • Homogeneous manifold
  • Rigidity
  • Semi-direct product

ASJC Scopus subject areas

  • Analysis
  • Geometry and Topology
  • Computational Theory and Mathematics


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