Take the 2-minute tour ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

Ok, we have the metric $ds^2=\frac{1}{y^2}$ defined in the upper half plane $U=\{(x,y)\in\mathbb{R}^2|y>0\}$.

I know two geodesics are $x(t)=a-b\cos{t}$ and $y(t)=b\sin{t}$. What are some others? And why would they be geodesics of this metric? (Particularly this second question is important.)

share|improve this question
add comment

1 Answer

up vote 3 down vote accepted

This is the hyperbolic metric in the upper-half plane and we know that the geodesic of this model are the half-circles orthogonal to the $x$-axis and the vertical lines

share|improve this answer
add comment

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.