Find the normal curvature and find the principal vectors

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Reference no: EM13697530

Find the normal curvature and find the principal vectors at the point given.

Let S be the embedded torus with parametrization

σ (θ, φ) = ((2 + cosθ) cosφ, (2 + cosθ)sinφ, sinθ).

The first and the second fundamental forms of σ are

dθ² + (2 + cosθ)²dφ² and dθ² + (2 + cosθ) cosθdφ²

Let p = (1,0,0) be a point on the torus.

(a) Find the normal curvature k_n(p, v) in the direction of the tangent vector

v = (0, 3, 2) ∈ T_pS.

(b) Find the principal vectors at the point p.

Reference no: EM13697530

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