Q1. (a) Find the intrinsic equations for a = (t - sint, 1- cost, t) (b)....

 

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Q1. (a) Find the intrinsic equations for a = (t - sint, 1- cost, t) (b). Derive the metric for (x', x2) where x 2(x')2 + x?, x = -x + 3x?? Also find the Christofell's symbols? Q2. Verify the Gauss-Weingarten equations for the torus? Q3. Find the following for the hyperboloid of one sheet (a) First and second fundamental forms (b) Normal curvature (c) Principal curvatures (d) Gaussian and Mean curvature? Q1. (a) Find the intrinsic equations for a = (t - sint, 1- cost, t) (b). Derive the metric for (x', x2) where x 2(x')2 + x?, x = -x + 3x?? Also find the Christofell's symbols? Q2. Verify the Gauss-Weingarten equations for the torus? Q3. Find the following for the hyperboloid of one sheet (a) First and second fundamental forms (b) Normal curvature (c) Principal curvatures (d) Gaussian and Mean curvature?