Abstract
It is shown that a connected Riemannian manifold has constant sectional curvature if and only if every one of its points is a non-degenerate maximum of some germ of smooth functions whose Riemannian gradient is a conformal vector field.
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Acknowledgements
The authors would like to thank the referee for several suggestions that substantially improved the exposition of the present work.
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Xiaoyang Chen was partially supported by the National Natural Science Foundation of China No. 11701427 and the Fundamental Research Funds for the Central Universities.
Frederico Xavier was Partially supported by the John William and Helen Stubbs Potter Professorship in Mathematics.
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Chen, X., Fontenele, F. & Xavier, F. A conformal characterization of manifolds of constant sectional curvature. Arch. Math. 116, 233–240 (2021). https://doi.org/10.1007/s00013-020-01542-4
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DOI: https://doi.org/10.1007/s00013-020-01542-4