A characterization of surfaces with their jacobi and simon operators

The aim of this thesis is to characterize the Euclidean rotational surfaces with their Jacobi and Simon operators. This thesis consists of 5 chapters. The first section is the introduction. Second chapter consist of some basic definitions which will be use in the other chapters. In the third chapter, calculations related to weak biharmonic submanifolds in R^n are given and the Jacobian mean curvature submanifolds are discussed. In the fourth chapter, rotation surfaces and Delaunay surfaces in R^3 are considered. Further, general rotation surfaces and rotation surfaces of 1. type and 2. type in R^4 are discussed. The Jacobi and Simon operators of them were investigated. The conditions of the specified surfaces to be weak biharmonic have been examined and some original results have been obtained. In addition, some examples supporting these results are given. In the fifth section, the results obtained in other sections are discussed and the results and suggestions are expressed.