g(x)= (x- tanh(x), sech(x))
Are those infinitely differentiable for all x?
i have a question to this exercise:
Show that the surface of revolution defined by this curve is a submanifold:
I could show, that this surface is a regular 2-dimensional submanifold.
Because the derivative of the parametrisation of the surface has at any point dimension 2.
But now i ask myself what about the smoothness of my submanifold? Is it a
surface? or only a . How can i decide about this question.
I hope you can help me in my problem.