## Question

###### (a) Show that if x(u,V) is a regular parametrisation ofa surface S such that E = G = f(u,v) and F = 0, then the Gaussian curvature isK = A(ln(f)) , 2 fwhere 4 = 82 + 02 denotes the Laplacian:(b) Compute the Gaussian curvature of the hyperbolic upper half-plane H: a sur- face with a regular parametrisation x: R x R+ ~t Hwith Elu,v) = G(u,0) = 2 for some a > 0,and F = 0

(a) Show that if x(u,V) is a regular parametrisation ofa surface S such that E = G = f(u,v) and F = 0, then the Gaussian curvature is K = A(ln(f)) , 2 f where 4 = 82 + 02 denotes the Laplacian: (b) Compute the Gaussian curvature of the hyperbolic upper half-plane H: a sur- face with a regular parametrisation x: R x R+ ~t Hwith Elu,v) = G(u,0) = 2 for some a > 0,and F = 0

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