A Characterization Of λ-Hypersurfaces in n-dimensional Euclidean Spaces

The aim of this thesis is to investigate the conditions for the rotational hypersurface and hypersurfaces with Monge patch in Euclidean spaces to become λ-hypersurface. 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 section, the calculations made so far regarding the hyper surfaces of R^(n+1) to be soliton, self similar and λ-hypersurface are given. The fourth section consists of the findings and consists of two sub-sections. First, the rotational hypersurfaces with R^(n+1) are second, and the hypersurfaces given by the monge patch in R^(n+1) are discussed. The conditions for these hypersurfaces to be compact and λ-hypersurfaces were examined and some original results were 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.