Stuck with problem: There is a local surface [tex]\alpha(u) = (f_1(u), f_2(u), f_3(u), f_4(u)) \in R^4[/tex]. I need to find basis vectors of tangent space on that surface in some point p. It is not difficult to calculate tangent space for that surface, we should choose some curve on the surface and then it's derivative, but how to find 3 vectors that will be a basis for tangent space? Is it Frenet trihedron? Can anyone give me a hint? Should be easy.