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Faculty of Sciences
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
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