Let M Rn be the graph of a function f : U Rn1 Rn parametrized by X: U Rn, X(u1,..., un1)
Chapter 8, Problem 15(choose chapter or problem)
Let M Rn be the graph of a function f : U Rn1 Rn parametrized by X: U Rn, X(u1,..., un1) = (u1,..., un1, f (u1,..., un1)). If N(u1,..., un1) = ( fu1 ,..., fun1 , 1) f 2 u1 ++ f 2 un1 + 1 is a unit normal, then the parametrization X is compatible with the (n 1)-form defined by X(u)(a1,..., an1) = det a1 an1 N .
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