(a) Let R7 be the Euclidean 7-space with cartesian coordinates (1, Y,.I3. Y3. and : M-R'...

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(a) Let R7 be the Euclidean 7-space with cartesian coordinates (1, Y,.I3. Y3. and : M-R' defined as p{u, v, w, z) = (v, u, u cos w, V3v cos w, u sin w, vV3v sin w, z), u, v 0; embeds M into R'. -(i) Find the basis of the tangent space of M. -(ii) Compute the metric on M induced by v. (a) Let R7 be the Euclidean 7-space with cartesian coordinates (1, Y,.I3. Y3. and : M-R' defined as p{u, v, w, z) = (v, u, u cos w, V3v cos w, u sin w, vV3v sin w, z), u, v 0; embeds M into R'. -(i) Find the basis of the tangent space of M. -(ii) Compute the metric on M induced by v.