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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… Click to show full abstract
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∈C1(M) are such that the set E:={x∈M|Hf(x)=h(x),Kf(x)=k(x)} is superdense at a certain point x0∈M, then Hk(x0)=Kh(x0).
Keywords:
generalization;
theorem equality;
mixed partial;
schwarz theorem;
equality mixed;
partial derivatives
Journal Title: Mathematische Nachrichten
Year Published: 2017
Link to full text (if available)
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Journal Title: Mathematische Nachrichten
Year Published: 2017
Link to full text (if available)
Share on Social Media: Sign Up to like & get
recommendations!