Given v_o in S^n show that there is an open neighborhood U in S^n of v_o and vector filds s_i : U——-> T(U) 1<= i<=n such that {s_1(v), ..., s_n (v)} is a basis of rhe vector space T_n (S^n) for all v in U
My attempt let v_o in S^n then v_o ^i not equal 0 in some i let say v_0 ^n+1 not equal 0 let pi : V_0 purp ——> R^n {0} I need to find a basis for v_0 purp How could I find the scaler lebmda s.t e_i + lebmda v_o will be in v_0purp Where { e_1,...e_n} basis for R^n