Differential Geometry

Find the torsion τ of the helix r(t) = (6 cos t, 6 sin t, 5t).

On a sphere of radius 2, a geodesic triangle has angle sum Σ. State Gauss–Bonnet and give the triangle's area.

Compute the total curvature ∮ κ ds of a circle of radius 4.

Write the first fundamental form (metric) of the sphere of radius 6 in spherical coordinates (θ, φ).

Find the principal curvatures and Gaussian curvature of a cylinder of radius 3.