Minimal Submanifolds Of Two Kinds Of Spaces

In the first part of this article, we mainly use the idea of analogical to spread the research methods from constant curvature space to the quasi-constant curvature space, which is to explore the suitable conditions about the infimum of the scalar curvature,then we can ensure the Riemannian manifold with quasi-constant curvature is a totally geodesic one.Let Mn be an compact sumanifold which is minimally immersed in a quasi-constant curvature Ricmann geometry Nn+P, where R denotes the scalar curvature of Mn, either or(2)R>[3p-2(b-a)np]+(n2-n)a+(n-1)(b+\b\)-[6p-4(3n+1)p](b-\b\). Then M is a totally geodesic submanifold. Here, a, b satisfies Kijkl=a(gikgjl-gilgjk)+b(gikλjλl+gjlλiλk-gilλjλk-gjkλiλl), and a,b,λi(i=1,2,...,n+p) are smooth function of NIn the second part, we give some kinds of minimal surfaces in the hyperbolic space with Ribaucour transformation.