Scaling of CAT(0) metric

33 Views Asked by At

Suppose $(X,d)$ is a geodesic metric space which satisfies CAT(0) inequality.Now if we rescale the metric $d$ then will it still be a CAT(0) metric space i.e, all geodesic triangles satisfies CAT(0) inequality.? here Scaling means $ d'(x,y) = \lambda d(x,y)$ for some $\lambda $ positive. I am confused as if a space is CAT(k) for some $k < 0$ then after rescaling the metric it will become CAT(-1).But i am getting stuck in this question. Thank you for any help in advance.