Chen’s Inequalities For Submanifolds

Abstract

In this thesis we studied one of the most important properties of a submanifold, namely the curvature that describes different geometrical and topological properties of a submanifold. We have three classes of submanifolds in a manifold 𝛭, and these classes are: 𝑖𝑚𝑚𝑒𝑟𝑠𝑒𝑑, 𝑖𝑚𝑏𝑒𝑑𝑑𝑒𝑑, 𝑎𝑛𝑑 𝑟𝑒𝑔𝑢𝑙𝑎𝑟. We discussed the basic equations for submanifold and fundamental theorems of submanifolds. We also investigated some special submanifolds, namely, minimal, totally geodesic, totally umbilical, totally real, CR (Cauchy Riemann) and parallel. In particular submanifolds of finite type in Euclidean space and Chen’s inequality have been treated and some results have been obtained.