Correction: Alshehri, N.; Guediri, M. Projective Vector Fields on Semi-Riemannian Manifolds. Mathematics 2024, 12, 2914

In our recent paper [1], we stated in Theorem 10 that on an n-dimensional semi-Riemannian manifold $(N,h)$ with $n\ge 2$, if P is a projective vector field that is also conformal, satisfying ${\pounds }_{P}h=2\psi h$, and the vector field $\zeta$, dual to $d\psi$, maintains a consistent causal character, then either P is homothetic or $\zeta$ is light-like.

However, it turns out that a case where the 1-form vector field $\zeta$ is light-like is not possible. Thus, the corrected statement of Theorem 10 is that a projective vector field that is also conformal on a semi-Riemannian manifold must be homothetic. We are grateful to Professor Graham Hall from the University of Aberdeen (Scotland, UK) for bringing this to our attention.

The authors state that the scientific conclusions are unaffected. This correction was approved by the Academic Editor. The original publication has also been updated.