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arXiv · 2211.08023

Biconservative surfaces in the $4$-dimensional Euclidean sphere

Simona Nistor·Cezar Oniciuc·Nurettin Cenk Turgay·Rüya Yeğin Şen
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Abstract

In this paper, we study biconservative surfaces with parallel normalized mean curvature vector field ($PNMC$) in the $4$-dimensional unit Euclidean sphere $\mathbb{S}^4$. First, we study the existence and uniqueness of such surfaces. We obtain that there exists a $2$-parameter family of non-isometric abstract surfaces that admit a (unique) $PNMC$ biconservative immersion in $\mathbb{S}^4$. Then, we obtain the local parametrization of these surfaces in the $5$-dimensional Euclidean space $\mathbb{E}^5$.

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Simona Nistor, Cezar Oniciuc, Nurettin Cenk Turgay, Rüya Yeğin Şen. 2022-11-15. Biconservative surfaces in the $4$-dimensional Euclidean sphere. https://arxiv.org/abs/2211.08023

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