Kozłowski, Wojciech \(\nabla\)-flat functions on manifolds. (English) Zbl 1098.53013 Ann. Pol. Math. 84, No. 2, 177-180 (2004). Let \(M\) be a connected real analytic manifold endowed with an affine connection \(\nabla\). The author proves that a smooth function that is pointwise \(\nabla\)-flat is real analytic and \(\nabla\)-flat. Also, he shows that the ring of all \(\nabla\)-flat functions on \(M\) is an integral domain. Finally, when \(M\) is a complete Riemannian manifold and \(\nabla\) is the Levi-Civita connection on \(M\), he proves that any \(\nabla\)-flat and bounded function on \(M\) is a constant. Reviewer: Aurel Bejancu (Safat) MSC: 53B05 Linear and affine connections 53B20 Local Riemannian geometry Keywords:affine connection; Levi-Civita connection; \(\nabla\)-flat functions PDFBibTeX XMLCite \textit{W. Kozłowski}, Ann. Pol. Math. 84, No. 2, 177--180 (2004; Zbl 1098.53013) Full Text: DOI