Poincaré’s Lemma on Some Non-Euclidean Structures

Research output: Contribution to journalArticle


The author proves the Poincaré lemma on some (n + 1)-dimensional corank 1 sub-Riemannian structures, formulating the (n−1)n(n2+3n−2)8 necessarily and sufficiently “curl-vanishing” compatibility conditions. In particular, this result solves partially an open problem formulated by Calin and Chang. The proof in this paper is based on a Poincaré lemma stated on Riemannian manifolds and a suitable Cesàro-Volterra path integral formula established in local coordinates. As a byproduct, a Saint-Venant lemma is also provided on generic Riemannian manifolds. Some examples are presented on the hyperbolic space and Carnot/Heisenberg groups.

Original languageEnglish
Pages (from-to)297-314
Number of pages18
JournalChinese Annals of Mathematics. Series B
Issue number2
Publication statusPublished - Mar 1 2018


  • Cesàro-Volterra path integral
  • Poincaré lemma
  • Sub-Riemannian manifolds

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

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