How does a metric of the form $\mathrm{d}z \mathrm{d}\bar z$ work, if $z$ and $\bar z$ are not independent?
104122
Complex coordinates in CFT
136936
How do you tell if a metric is curved?
42361
Why do we use the Euclidean metric on $\mathbb{R}^2$?
22133
Why is the covariant derivative of the determinant of the metric zero?
65809
Show that $d_2$ defined by $d_2(x,y)=\frac{|x-y|}{1+|x-y|}$ is a metric
49503
Why does the natural quotient metric works in this case?
37840
Does the Levi-Civita connection determine the metric?
137881
A not complete metric space?
94672
Why is the triangle inequality property important for metric spaces?
140692
Existence of a complete metric on $(0,1)$
59833
Isometric embedding of Schwarzchild metric in $\mathbb{R}^4$
127034
Let $\rho(x,y)= \frac{d(x,y)}{1+d(x,y)}$, show that $\rho$ is a metric equivalent to $d$
123039
If $0<\alpha < 1$ and $d(x,y)$ is metric, show that $((d(x,y))^{\alpha}$ is metric.
132528
Are metrics that determine the same topology, equivalent?
65840
Norm induced by metric
26547
Real numbers equipped with the metric $ d (x,y) = | \arctan(x) - \arctan(y)| $ is an incomplete metric space
146215
Metric on a Quotient of the Riemann Sphere