The author proves the Poincard lemma on some （n ＋1）-dimensional corank 1 sub-Riemannian structures, formulating the （n-1）n（n2＋3n-2） necessarily and sufficient- s ly ＂curl-vanishing＂ compatibility conditions...The author proves the Poincard lemma on some （n ＋1）-dimensional corank 1 sub-Riemannian structures, formulating the （n-1）n（n2＋3n-2） necessarily and sufficient- s ly ＂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 Poincard lemma stated on l：tiemannian manifolds and a suitable Ceskro-Volterra path in- tegral 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.展开更多
文摘The author proves the Poincard lemma on some （n ＋1）-dimensional corank 1 sub-Riemannian structures, formulating the （n-1）n（n2＋3n-2） necessarily and sufficient- s ly ＂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 Poincard lemma stated on l：tiemannian manifolds and a suitable Ceskro-Volterra path in- tegral 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.
