Uma caracterização do produto Sk (cos θ) x Sn-k (sen θ) na esfera euclidiana S^ (n+1)

Abstract

In this paper we consider n-dimensional hypersurfaces with constant scalar curvature in the unit sphere S ^ (n +1). Characterize the hypersurfaces given by products of spheres whose size is n, the unit sphere S ^ (n +1) and show that there is more compact hypersurfaces with constant scalar curvature in the unit sphere S ^ (n +1) that are not congruent itself. In particular, prove that M is an n-dimensional hypersurface (n> 3) complete with buckle locally flat accordingly constant scalar n (n-1) on the unit sphere S r ^ (n +1) is greater than r a pre-established and two results are proven value, and the other one involving isometries of existence, when are S satisfy certain conditions, where S is the square of the standard is second fundamental form of M.