Biharmonic PNMCV submanifolds in Euclidean 5-space

Rüya Şen; Nurettin Cenk Turgay

doi:10.55730/1300-0098.3361

Biharmonic PNMCV submanifolds in Euclidean 5-space

Rüya Şen^*
, Nurettin Cenk Turgay

^*Corresponding author for this work

Department of Mathematics Engineering

Istanbul Medeniyet University

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

6 Citations (Scopus)

Abstract

In this article, we study 3-dimensional biconservative and biharmonic submanifolds of E⁵ with parallel normalized mean curvature vector (PNMCV). First, we prove that the principal curvartures and principal directions of biconservative PNMCV isometric immersions into E⁵ can be determined intrinsically. Then, we complete the proof of Chen’s biharmonic conjecture for PNMCV submanifolds of E⁵.

Original language	English
Pages (from-to)	296-316
Number of pages	21
Journal	Turkish Journal of Mathematics
Volume	47
Issue number	1
DOIs	https://doi.org/10.55730/1300-0098.3361
Publication status	Published - 2023

Bibliographical note

Publisher Copyright:
© TÜBİTAK

Keywords

Biconservative submanifolds
Biharmonic submanifolds
Parallel normalized mean curvature vectors

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10.55730/1300-0098.3361

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abstract = "In this article, we study 3-dimensional biconservative and biharmonic submanifolds of E5 with parallel normalized mean curvature vector (PNMCV). First, we prove that the principal curvartures and principal directions of biconservative PNMCV isometric immersions into E5 can be determined intrinsically. Then, we complete the proof of Chen{\textquoteright}s biharmonic conjecture for PNMCV submanifolds of E5.",

keywords = "Biconservative submanifolds, Biharmonic submanifolds, Parallel normalized mean curvature vectors",

author = "R{\"u}ya {\c S}en and Turgay, \{Nurettin Cenk\}",

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AU - Turgay, Nurettin Cenk

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PY - 2023

Y1 - 2023

N2 - In this article, we study 3-dimensional biconservative and biharmonic submanifolds of E5 with parallel normalized mean curvature vector (PNMCV). First, we prove that the principal curvartures and principal directions of biconservative PNMCV isometric immersions into E5 can be determined intrinsically. Then, we complete the proof of Chen’s biharmonic conjecture for PNMCV submanifolds of E5.

AB - In this article, we study 3-dimensional biconservative and biharmonic submanifolds of E5 with parallel normalized mean curvature vector (PNMCV). First, we prove that the principal curvartures and principal directions of biconservative PNMCV isometric immersions into E5 can be determined intrinsically. Then, we complete the proof of Chen’s biharmonic conjecture for PNMCV submanifolds of E5.

KW - Biconservative submanifolds

KW - Biharmonic submanifolds

KW - Parallel normalized mean curvature vectors

UR - https://www.scopus.com/pages/publications/85147760488

U2 - 10.55730/1300-0098.3361

DO - 10.55730/1300-0098.3361

M3 - Article

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EP - 316

JO - Turkish Journal of Mathematics

JF - Turkish Journal of Mathematics

IS - 1

ER -

Biharmonic PNMCV submanifolds in Euclidean 5-space

Abstract

Bibliographical note

Keywords

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