Table of Contents
ISRN Geometry
Volume 2012 (2012), Article ID 591296, 23 pages
http://dx.doi.org/10.5402/2012/591296
Research Article

On Some 𝐿 π‘˜ -Finite-Type Euclidean Hypersurfaces

Department of Pure Mathematics, Faculty of Mathematical Sciences, Tarbiat Modares University, P.O. Box 14115-134, Tehran, Iran

Received 24 May 2012; Accepted 26 July 2012

Academic Editors: I. Biswas, A. Ferrandez, and G. Martin

Copyright © 2012 Akram Mohammadpouri and S. M. B. Kashani. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We study some 𝐿 π‘˜ -finite-type Euclidean hypersurfaces. We classify 𝐿 π‘˜ -1-type Euclidean hypersurfaces and 𝐿 π‘˜ -null-2-type Euclidean hypersurfaces with at most two distinct principal curvatures. We also prove that, under some mild restrictions, there exists no 𝐿 π‘˜ -null-3-type Euclidean hypersurface.