I was studying the metric tensor and saw all about degenerate metrics. I would like what is the physical or geometrical intuition of a degenerate metric.
What is the meaning of $g(v,w) = 0$ for a fixed $vec{v}$ vector and any $vec{w}$ vector? Because there is a vector orthogonal to all others. I understand that for matrix form, you can study if a metric is degenerate or not with the determinant of its matrix form.
When I studied determinant and linear dependence, I saw that if a determinant was 0, it is because the transformation degenerates the space, and turns it into a lower dimensional space. Since metrics can be used to describe space, what sense does it make for a metric to be degenerate, that is, for its determinant to be 0? I also don't understand what relation exists that the determinant is 0 with $g(v,w) = 0$ for a fixed $vec{v}$ vector and any $vec{w}$ vector. Thanks in advance
