Details

Autor(en) / Beteiligte

• Fu, Yu

Titel

The study on surfaces immersed in space forms

Ort / Verlag

ProQuest Dissertations & Theses

Erscheinungsjahr

2010

Quelle

ProQuest Dissertations & Theses A&I

Beschreibungen/Notizen

• Translation from original language as provided by authorThe research presented in this thesis belongs to the theory of submanifolds in diffential geometry. Our main content contains: the equiaffne theory for surfaces in affine 4-dimensional space; the theory for slant surfaces in Lorentzian complex space forms; the theory for Lorentzian surfaces in pseudo-Riemannian space forms. In Chapter 3, according to the equiaffine theory for nondegenerate surfaces in R4 established by Nomizu and Vrancken, we study some classification problems on affine maximal surfaces, locally symmetric surfaces and affine spheres. Under the condition that induced connection is fat, we completely classify affine maximal surfaces in R4. Under the additional condition that affine normal bundle is fat, we completely classify locally symmetric surfaces in R4. In addition, under the condition r?g? = 0, we characterize all the affine spheres with nonzero constant length mean curvature vector, which indicates that there is great difference be