Comment on "Dark matter as a Weyl geometric effect"

In this note we comment on a recent attempt by P. Burikham, T. Harko, K. Pimsamarn and S. Shahidi [Phys. Rev. D {\bf 107}, 064008 (2023)] to explain the galactic rotation curves as the result of the motion of time-like test particles in the Weyl geometric theory of gravity. We show that the static, spherically symmetric solution found by the authors, which could be the basis of an alternative explanation of the galactic rotation curves, is wrong.