Hi there. I'm trying to understand the Second Fundamental Form but I'm stuck on something. Let:
is a parameterised form of a surface.
It's written where is the normal vector to the surface.
I don't understand what is and
This is just the decomposition of in a basis. Indeed, is a basis of the tangent plane, while is orthogonal to that plane, so that is a basis of (which depends on ). Then for instance is the -component of .
This is just the decomposition of in a basis. Indeed, is a basis of the tangent plane, while is orthogonal to that plane, so that is a basis of (which depends on ). Then for instance is the -component of .
Never mind. It's explained 3 chapters ahead. It's the Christoffel symbol.