I have seen and gone through this thread over and over again but still it is not clear. https://www.physicsforums.com/threads/vectors-one-forms-and-gradients.82943/ The gradient in different coordinate systems is dependent on a metric But the 1-form is not dependent on a metric. It is a metric independent mapping. Is that correct first of all ? But I also see that the 1-form is defined in term of a gradient. Is that accurate ? So is the 1-form dependent on a metric ? I am really confused. So any clarifications would help.