Week 44

This week we have covered the basic material needed for the study of differential geometry.  First the definition of tangent planes and derivatives of maps and functions in 5.1, and then the structure that all the remaining theory will depend on - the Riemannian metric  (5.3).  Finally we also introduced the maps that preserve the Riemannian structure, isometries.  Locally the metric can be described in terms of the inner products of basis vectors coming from local paramerizations, giving rise to three functions usually denoted E, F and G.  It is important that you become familiar with these from the beginning.   

Exercises for Tuesday November 4:  5.1: 3, 4,   5.3: 1, 3, 4.