A note on a generalization of the Schwarz theorem about the equality of mixed partial derivatives

作者：Delladio Silvano^*

来源：Mathematische Nachrichten, 2017, 290(11-12): 1630-1636.

DOI：10.1002/mana.201600195

• Superdensity
• equality of mixed partial derivatives

We provide a generalization of the classical Schwarz theorem about the equality of mixed partial derivatives. More precisely we extend it to a Riemannian manifold (M,g), by proving the following statement: if H,K is a couple of commuting vector fields on M and f,h,k is an element of C-1(M) are such that the set E:={x is an element of M vertical bar Hf(x)=h(x),Kf(x)=k(x)} is superdense at a certain point x(0) is an element of M, then Hk(x(0))=Kh(x(0)).

• 出版日期2017-8