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

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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.

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Author information

Authors and Affiliations

  1. School of Mathematics and Quantitative Economics, Dongbei University of Finance and Economics, Dalian, 116025, P.R. China

    Yu Fu

  2. Al. I. Cuza University of Iasi, Bd. Carol I, n. 11, 700506, Iasi, Romania

    Marian Ioan Munteanu

Authors
  1. Yu Fu
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  2. Marian Ioan Munteanu
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Corresponding author

Correspondence to Marian Ioan Munteanu.

Additional information

Dedicated to Professor Bang-Yen Chen with the occasion of his 70th birthday.

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Fu, Y., Munteanu, M.I. Generalized constant ratio surfaces in \(\mathbb{E}^3 \) . Bull Braz Math Soc, New Series 45, 73–90 (2014). https://doi.org/10.1007/s00574-014-0041-2

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  • DOI: https://doi.org/10.1007/s00574-014-0041-2

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