Let Mⁿ be a closed submanifold isometrically immersed in a unit sphere S^n+p. Denote by R, H and S, the normalized scalar curvature, the mean curvature, and the square of the length of the second fundamental form of Mⁿ, respectively. Suppose R is constant and ≥1. We study the pinching problem on S and prove a rigidity theorem for Mⁿ immersed in S^n+p with parallel normalized mean curvature vector field. When n≥8 or, n=7 and p≤2, the pinching constant is best.

The goal of this investigation was to find the major determinants of married women participation in the urban area labour force in Zhejiang (China) and Brazzaville (Congo). The methodology used in this study is correct and the resulting conclusion is that the participation of married women basically depends on her personal and family characteristics. Age, education, presence of additional adult in the family are important factors in Brazzaville and Zhejiang. However, the number of children significantly affects only Brazzaville urban married women.