Document Details Document Type : Article In Journal  Document Title : Extrinsic spheres in a real space form Extrinsic spheres in a real space form   Subject : Mthematics  Document Language : English  Abstract : Let M be an n-dimensional orientable compact hypersurface in an (n+1)-dimensional real space form M̄(c), n ≥2. If the lengths ∥ℝ∥, ∥double-struck A∥ and ∥∇α∥ of the curvature tensor field R, the shape operator A, the gradient ∇α of the mean curvature α and the scalar curvature S of the hypersurface M satisfy the inequality (Equation Presented) where δ = min Ric = min (Equation Presented) Ricp(v), Ric is Ricci curvature of the hypersurface, then it is shown that M is an extrinsic sphere in M̄(c). In particular we deduce that the condition 1/2 ∥R∥2 ≤ δ ∥A∥2 - n(n - 1) ∥∇α∥2 characterizes spheres in the Euclidean space Rn+l among the compact orientable hypersurfaces whose Ricci curvatures are bounded below by a constant δ > 0.  ISSN : 1370-1444  Journal Name : Bulletin of the Belgian Mathematical Society - Simon Stevin, Pages 269-275  Volume : 15  Issue Number : 2  Publishing Year : 2008 AH 2008 AD  Number Of Pages : 7  Article Type : Article  Added Date : Thursday, October 15, 2009  Researchers Researcher Name (Arabic) Researcher Name (English) Researcher Type Dr Grade Email Sharief Deshmukh Sharief Deshmukh Researcher Doctorate shariefd@ksu.edu.sa محمد حسن هيد Mohammad Hasan Shahid Researcher Doctorate hasan_jmi@yahoo.com Back To Researches Page