Search

This work is an initial attempt to extend to many-parameter families of smooth functions on a smooth manifold, and projections of smooth maps into subspaces of higher dimension, the well-known inter relations, between the space of Morse function on a smooth manifold and the space of immersions of the manifold in a cartesian space, which are given by the Gauss-maps of the immersions, and the orthogonal projections of the immersions onto lines in the Cartesian spaces. Results, both local and global, are obtained.

The subject matter of this thesis is concerned with the stability of fluid flows; more particularly , with the stability of liquid films which have an interface with air. We will therefore begin by formulating the basic equations and ideas which pertain to this class of problems. Later in this chapter, a summary will be given of the topics dealt with in this dissertation.