Biconservative surfaces in the 4-dimensional Euclidean sphere

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Nistor S., Oniciuc C., Turgay N. C., Yeğin Şen R.

Annali di Matematica Pura ed Applicata, 2023 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Publication Date: 2023
  • Doi Number: 10.1007/s10231-023-01323-0
  • Journal Name: Annali di Matematica Pura ed Applicata
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, MathSciNet, zbMATH
  • Keywords: Biconservative surfaces, Riemannian space forms, Parallel normalized mean curvature vector field
  • Istanbul Technical University Affiliated: Yes

Abstract

In this paper, we study biconservative surfaces with parallel normalized mean curvature vector field (PNMC) in the 4-dimensional unit Euclidean sphere S4. 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 S4. Then, we obtain the local parametrization of these surfaces in the 5-dimensional Euclidean space E5. We end the paper by proving that the substantial codimension of PNMC biconservative surfaces in Sn, n≥ 5 , is equal to 2.