I am going to give a talk in a seminar about the general theme 'sum of squares'. My interests lie in Differential Geometry, so I recalled that the curvature is a local invariant, an obstruction to the metric being locally a sum of squares of coordinate differentials.
Can some people suggest me some good books which clearly illustrate the relation between the curvature and the metric? Also, do you guys have other suggestions about 'sum of squares' in Geometry? Thanks a lot!