Small Perturbations and Infinitesimal Deformations on Surfaces of Revolution

Any given surface of revolution embedded in Euclidean three-space can always be perturbed by arbitrarily small ambient isotopies as to admit highly nontrivial vector fields inducing infinitesimal deformations. For this matter Morse Theory is used, clarifying and giving a general response of a problem started with an idea of M. Spivak.