On biconservative surfaces in 4-dimensional Euclidean space

Rüya Yeğin Şen; Nurettin Cenk Turgay

doi:10.1016/j.jmaa.2017.12.009

On biconservative surfaces in 4-dimensional Euclidean space

Rüya Yeğin Şen^*, Nurettin Cenk Turgay

^*Corresponding author for this work

Department of Mathematics Engineering

Istanbul Medeniyet University

Research output: Contribution to journal › Article › peer-review

15 Citations (Scopus)

Abstract

In this paper, we study non-CMC biconservative surfaces with flat normal bundle in the Euclidean 4-space E⁴. First, we determine locally all parallel normalized mean curvature vector (PNMCV) biconservative surfaces in E⁴, showing that they are certain rotational surfaces. Then, we consider meridian surfaces lying on a rotational hypersurface of E⁴ and construct a family of biconservative surfaces with flat normal bundle and non-parallel normalized mean curvature vector.

Original language	English
Pages (from-to)	565-581
Number of pages	17
Journal	Journal of Mathematical Analysis and Applications
Volume	460
Issue number	2
DOIs	https://doi.org/10.1016/j.jmaa.2017.12.009
Publication status	Published - 15 Apr 2018

Bibliographical note

Publisher Copyright:
© 2017 Elsevier Inc.

Funding

This work was obtained during the project supported by Research Fund of the Istanbul Medeniyet University (Project Number: F-GAP-2017-986 ).

Funders	Funder number
Istanbul Medeniyet University	F-GAP-2017-986

Keywords

Biconservative surfaces
Meridian surfaces
Parallel normalized mean curvature vectors

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10.1016/j.jmaa.2017.12.009

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AU - Turgay, Nurettin Cenk

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AB - In this paper, we study non-CMC biconservative surfaces with flat normal bundle in the Euclidean 4-space E4. First, we determine locally all parallel normalized mean curvature vector (PNMCV) biconservative surfaces in E4, showing that they are certain rotational surfaces. Then, we consider meridian surfaces lying on a rotational hypersurface of E4 and construct a family of biconservative surfaces with flat normal bundle and non-parallel normalized mean curvature vector.

KW - Biconservative surfaces

KW - Meridian surfaces

KW - Parallel normalized mean curvature vectors

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ER -

On biconservative surfaces in 4-dimensional Euclidean space

Abstract

Bibliographical note

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Keywords

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