ABSTRACT
Intrinsic geometry is a property of surfaces that depend entirely on the metric coefficients of the regular. Since intrinsic properties do not depend on a normal vector to a surface at a point, then such properties apply to any surface as long as we have a metric tensor. This chapter discusses a number of definitions and theorems about curves and surfaces to Euclidean n-dimensional space. The Fundamental Theorem of Space Curves immediately generalizes to an n-dimensional case. For some surfaces that arise as the image of a single parametrized function, not necessarily a bijection, it may be easy to check if the surface is orientable. Many local properties and definitions have immediate generalizations to curves in n-dimensional Euclidean space.
