IJPAM: Volume 77, No. 5 (2012)

REMARKS ON HYPERSURFACES OF
REVOLUTION IN EUCLIDEAN SPACE $\mathbb{R}^{n+1}$

Zonglao Zhang
College of Mathematics and Information Science
Wenzhou University
Wenzhou, Zhejiang, 325035, P.R. CHINA


Abstract. We investigate hypersurfaces in Euclidean space $\mathbb{R}^{n+1}$. Two main results are obtained, one concerns the Gauss-Kronecker curvature of a graph defined by a radially symmetric function on $\mathbb{R}^{n}$, and the other gives a sufficient and necessary condition for a hypersurfaces to be hypersurfaces of revolution.

Received: September 5, 2011

AMS Subject Classification: 53A07, 53C45, 53C40

Key Words and Phrases: hypersurface of revolution, Gauss-Kronecker curvature, convex hypersurface, sectional curvature

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Source: International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2012
Volume: 77
Issue: 5