Lab 6: Extrinsic Theory of SurfacesIntroduction
Properties of surfaces in space that only depend on measurements of length
are called
intrinsic
. We have seen that such properties include the angle between two different
smooth curves through a point and the area of a region. In this laboratory,
we study
extrinsic
properties, those properties which need more than just metric considerations.
It will turn out that some of the properties that are initially defined using
extrinsic concepts are in fact intrinsic, and when that happens, it is a major
theorem in differential geometry.
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