A geometric perspective on the piola identity in Riemannian settings

Raz Kupferman, Asaf Shachar*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

4 Scopus citations


The Piola identity div cof ∇f = 0 is a central result in the mathematical theory of elasticity. We prove a generalized version of the Piola identity for mappings between Riemannian manifolds, using two approaches, based on different interpretations of the cofactor of a linear map: one follows the lines of the classical Euclidean derivation and the other is based on a variational interpretation via Null-Lagrangians. In both cases, we first review the Euclidean case before proceeding to the general Riemannian setting.

Original languageAmerican English
Pages (from-to)59-76
Number of pages18
JournalJournal of Geometric Mechanics
Issue number1
StatePublished - Mar 2019

Bibliographical note

Publisher Copyright:
© American Institute of Mathematical Sciences


  • Differential geometry
  • Elasticity
  • Null-Lagrangians
  • Piola identity
  • Riemannian geometry


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