A study of the rigidity and inflexibility of analytic surfaces of revolution with flattening at the pole (Q1096186)

The author studies questions of local rigidity of analytic surfaces of revolution in a neighborhood of a point with vanishing Gaussian curvature. He shows that, quite remarkably, the analytic deformations can be found by obtaining integer solutions of a certain Diophantine equation (namely, Pell's equation). He gives applications of this result by formulating conditions of rigidity and nonrigidity in the classes of analytic, \(C^{\infty}\)-, and \(C^ q\)-deformations, \(q<\infty\).