I'm confused with these definitions. The metric of certain space and the second fundamental form seem to be the same object.
I don't know what else to say, this is a pretty straight forward question.
I'm confused with these definitions. The metric of certain space and the second fundamental form seem to be the same object.
I don't know what else to say, this is a pretty straight forward question.
The first fundamental form and the metric tensor are indeed one and the same. The second fundamental form is not. It's a sort of derivative of the metric tensor.