## Busemann function on Hyperbolic space [closed]

Possible Duplicate:
laplacian of Busemann function on hyperbolic space

What's the laplacian of the Buseman function on Hyperbolic space H^n?=n-1?When restricted to geodesics,is it linear?And the level sets are totally geodesic?

-
 the tag "differential-geometry" should really be replaced by the standard one "dg.differential-geometry" – YangMills Oct 15 at 13:42 These are fundamental questions about the Busemann function that can be answered using different approaches. On one hand, it's a good exercise for any serious student of Riemannian geometry. On the other, I'm pretty sure you can find the answer or the means of finding the answer from any number of textbooks. One way is to use the metric written in polar co-ordinates to answer the question for the distance function from a fixed point and take a limit. Another way is to work with Jacobi fields. – Deane Yang Oct 15 at 14:06 An important word to look up and understand is "horosphere" or if $n = 2$, "horocycle". – Deane Yang Oct 15 at 14:16 Why are you posting a duplicate? – Igor Rivin Oct 15 at 16:05 Sorry that I think I am too lazy.I can manage it now.Thank you for your answer.It's time to close it. – jiangsaiyin Oct 16 at 6:22