Compact Hypersurface With Constant Average Curvature In The Quasi-constant Curvature Space

In the thesis, properties of hypersurfaces in the quasi-constant cur-vature space were investigated. There are three sections in total, which describe our work in details.In section Ⅰ, the motivation and academic background of the thesis are introduced.In section Ⅱ, first of all. we will introduce some fundamental concepts of differential geometry. Secondly, some important lemmas which related our work are also presented. Thirdly, the closely-related equations are described comprehensively.In section Ⅲ, the compact hypersurfaces with the constant average curvature in the quasi-constant curvature space are studied. Two funda-mental properties and corresponding inference are obtained as the impor-tant conclusion.