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Example plot

Equations

x(u, v) = a cos(u) cosh(v/a)
y(u, v) = a sin(u) cosh(v/a)
z(u, v) = v

Surface properties

g = 0

ds^2 = a^2 cosh^2(v/a) du^2 + cosh^2(v/a) dv^2

dA = a cosh^2(v/a) du dv

x^_ = (0, 0, 0)

K(u, v) = -(sech^4(v/a))/a^2

Metric properties

g_(uu) = a^2 cosh^2(v/a)
g_(vv) = cosh^2(v/a)

Γ | u |
| | uv = tanh(v/a)/a
Γ | u |
| | vu = tanh(v/a)/a
Γ | v |
| | uu = -a tanh(v/a)
Γ | v |
| | vv = tanh(v/a)/a

E(u, v) = a^2 cosh^2(v/a)
F(u, v) = 0
G(u, v) = cosh^2(v/a)

e(u, v) = -a
f(u, v) = 0
g(u, v) = 1/a

Vector properties

left double bracketing bar x(u, v) right double bracketing bar = sqrt(a^2 cosh((2 v)/a) + a^2 + 2 v^2)/sqrt(2)

N^^(u, v) = (-cos(u) sech(v/a), -sech(v/a) sin(u), tanh(v/a))

Properties

minimal surfaces | surfaces of revolution