【作者】 王明明；

【导师】 郝建华；

【作者基本信息】 山西师范大学 ， 基础数学， 2012， 硕士

【摘要】 本文研究了紧致极小超曲面的一些性质.全文共四章.第一章是引言,介绍了微分几何这门学科的发展史和本文的主要结果.第二章介绍了微分几何学中的一些主要概念和重要引理.第三章介绍了等距浸入子流形的基本方程.第四章主要对紧致极小超曲面的性质进行了讨论.首先对文献[3]中介绍了的定理给出了等价条件,并推广了其结论,其次对拟常曲率空间中的紧致极小超曲面进行了讨论,最后讨论了常截面曲率为1的紧致极小超曲面,得到了一些新结论.更多还原

【Abstract】 In this thesis, some properties of compact minimal hypersurface areinvestigated and analyzed in four chapters.In chapterⅠ, the history of diferential geometry is overviewed. Thenthe task and contributions of this thesis are presented.In chapterⅡ, some related concepts and important lemmas of difer-ential geometry are introduced as the basis of our work.In chapterⅢ, the basic equations of isometric immersed submanifoldare discussed.In the last chapter, the properties of compact minimal hypersurfaceare studied. Firstly, the equivalent conditions of the important theoremwhich was described in the literature are derived and its conclusions arepromoted. Secondly, the compact minimal hypersurface in the quasi con-stant curvature space is invertigated. Finally, some new conclusions areobtained from the compact minimal hypersurface when the value of con-stant sectional curvature equals to one.更多还原