Lab 6: Extrinsic Theory of Surfaces

Introduction

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.