Biconservative surfaces in the 4-dimensional Euclidean sphere

Creative Commons License

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

Annali di Matematica Pura ed Applicata, cilt.202, sa.5, ss.2345-2377, 2023 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 202 Sayı: 5
  • Basım Tarihi: 2023
  • Doi Numarası: 10.1007/s10231-023-01323-0
  • Dergi Adı: Annali di Matematica Pura ed Applicata
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, MathSciNet, zbMATH
  • Sayfa Sayıları: ss.2345-2377
  • Anahtar Kelimeler: Biconservative surfaces, Riemannian space forms, Parallel normalized mean curvature vector field
  • İstanbul Teknik Üniversitesi Adresli: Evet

Özet

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.