High order covariant derivatives are not symmetric in all arguments in general. [1]

References Link to heading

1. HeroZhang001, Answer to “Is the $k$th covariant derivative of a function $f\colon M\to\mathbb R$ symmetric?”, May. 16, 2024. [Online]. Available: https://math.stackexchange.com/a/4917638/1516753 [Accessed: Feb. 3, 2025].