Biconservative surfaces in the 4-dimensional Euclidean sphere

Simona Nistor; Cezar Oniciuc; Nurettin Cenk Turgay; Rüya Yeğin Şen

doi:10.1007/s10231-023-01323-0

Biconservative surfaces in the 4-dimensional Euclidean sphere

Simona Nistor^*
, Cezar Oniciuc
, Nurettin Cenk Turgay
, Rüya Yeğin Şen

^*Bu çalışma için yazışmadan sorumlu yazar

Matematik Bölümü

Araştırma sonucu: Dergiye katkı › Makale › bilirkişi

3 Atıf (Scopus)

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.

Orijinal dil	İngilizce
Sayfa (başlangıç-bitiş)	2345-2377
Sayfa sayısı	33
Dergi	Annali di Matematica Pura ed Applicata
Hacim	202
Basın numarası	5
DOI'lar	https://doi.org/10.1007/s10231-023-01323-0
Yayın durumu	Yayınlandı - Eki 2023

Bibliyografik not

Publisher Copyright:
© 2023, Fondazione Annali di Matematica Pura ed Applicata and Springer-Verlag GmbH Germany, part of Springer Nature.

Finansman

The first author was supported by a grant of the Romanian Ministry of Research and Innovation, CNCS - UEFISCDI, project number PN-III-P11.1-PD-2019-0429, within PNCDI III. The third and fourth named authors were supported by a 3501 project of the Scientific and Technological Research Council of Türkiye (TÜBİTAK) (Project Number: 121F253).

Finansörler	Finansör numarası
Corporation for National and Community Service
Ontario Ministry of Research, Innovation and Science
Türkiye Bilimsel ve Teknolojik Araştırma Kurumu	121F253
Unitatea Executiva pentru Finantarea Invatamantului Superior, a Cercetarii, Dezvoltarii si Inovarii	PN-III-P11.1-PD-2019-0429

Belgeye Erişim

10.1007/s10231-023-01323-0

Diğer Dosyalar ve Linkler

Link to publication in Scopus

Alıntı Yap

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title = "Biconservative surfaces in the 4-dimensional Euclidean sphere",

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.",

keywords = "Biconservative surfaces, Parallel normalized mean curvature vector field, Riemannian space forms",

author = "Simona Nistor and Cezar Oniciuc and Turgay, \{Nurettin Cenk\} and \{Yeğin {\c S}en\}, R{\"u}ya",

note = "Publisher Copyright: {\textcopyright} 2023, Fondazione Annali di Matematica Pura ed Applicata and Springer-Verlag GmbH Germany, part of Springer Nature.",

year = "2023",

month = oct,

doi = "10.1007/s10231-023-01323-0",

language = "English",

volume = "202",

pages = "2345--2377",

journal = "Annali di Matematica Pura ed Applicata",

issn = "0373-3114",

publisher = "Springer Nature",

number = "5",

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TY - JOUR

T1 - Biconservative surfaces in the 4-dimensional Euclidean sphere

AU - Nistor, Simona

AU - Oniciuc, Cezar

AU - Turgay, Nurettin Cenk

AU - Yeğin Şen, Rüya

PY - 2023/10

Y1 - 2023/10

N2 - 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.

AB - 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.

KW - Biconservative surfaces

KW - Parallel normalized mean curvature vector field

KW - Riemannian space forms

UR - https://www.scopus.com/pages/publications/85151249630

U2 - 10.1007/s10231-023-01323-0

DO - 10.1007/s10231-023-01323-0

M3 - Article

AN - SCOPUS:85151249630

SN - 0373-3114

VL - 202

SP - 2345

EP - 2377

JO - Annali di Matematica Pura ed Applicata

JF - Annali di Matematica Pura ed Applicata

IS - 5

ER -

Biconservative surfaces in the 4-dimensional Euclidean sphere

Özet

Bibliyografik not

Finansman

Belgeye Erişim

Diğer Dosyalar ve Linkler

Parmak izi

Alıntı Yap