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Generalized constant ratio surfaces in $\mathbb{E}^3 $

Generalized constant ratio surfaces in $\mathbb{E}^3 $ It iswell-known that the positionvector function is themost basic geometric object for a surface immersed in the three dimensional Euclidean space $\mathbb{E}^3 $ . In 2001, B.-Y. Chen defined constant ratio hypersurfaces in Euclidean n-spaces. Independently, in 2010, by using another approach in dimension 3, the second author classified constant slope surfaces. In this paper, we extend this concept in order to study surfaces with the property that the tangential component of the position vector is a principal direction on the surface. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Bulletin of the Brazilian Mathematical Society, New Series Springer Journals

Generalized constant ratio surfaces in $\mathbb{E}^3 $

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References (37)

Publisher
Springer Journals
Copyright
Copyright © 2014 by Sociedade Brasileira de Matemática
Subject
Mathematics; Mathematics, general; Theoretical, Mathematical and Computational Physics
ISSN
1678-7544
eISSN
1678-7714
DOI
10.1007/s00574-014-0041-2
Publisher site
See Article on Publisher Site

Abstract

It iswell-known that the positionvector function is themost basic geometric object for a surface immersed in the three dimensional Euclidean space $\mathbb{E}^3 $ . In 2001, B.-Y. Chen defined constant ratio hypersurfaces in Euclidean n-spaces. Independently, in 2010, by using another approach in dimension 3, the second author classified constant slope surfaces. In this paper, we extend this concept in order to study surfaces with the property that the tangential component of the position vector is a principal direction on the surface.

Journal

Bulletin of the Brazilian Mathematical Society, New SeriesSpringer Journals

Published: Apr 8, 2014

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