TRANSFORMATION GROUPS AND GROUP ACTION

Abstract

In this study we introduced Lie groups and Lie algebra . It was found out that , for a given variation ,described via Lie groups, the Lie algebra of that group gave rise to the invariants of the variations. We utilized the invariants to solve some problems in geometry and physics.. In particular we handled symmetric spaces, physical invariantsand partial differential equations. Thus the main problem discussed by this thesis is How to use invariants in solving variants or classifying them.