Biharmonic PNMCV submanifolds in Euclidean 5-space

Authors

RÜYA ŞEN
NURETTİN CENK TURGAY

Abstract

In this article, we study 3-dimensional biconservative and biharmonic submanifolds of $\mathbb{E}^5$ with parallel normalized mean curvature vector (PNMCV). First, we prove that the principal curvartures and principal directions of biconservative PNMCV isometric immersions into $\mathbb{E}^5$ can be determined intrinsically. Then, we complete the proof of Chen's biharmonic conjecture for PNMCV submanifolds of $\mathbb{E}^5$.

DOI

10.55730/1300-0098.3361

Keywords

Biharmonic submanifolds, biconservative submanifolds, parallel normalized mean curvature vectors

First Page

296

Last Page

316

Recommended Citation

ŞEN, RÜYA and TURGAY, NURETTİN CENK (2023) "Biharmonic PNMCV submanifolds in Euclidean 5-space," Turkish Journal of Mathematics: Vol. 47: No. 1, Article 20. https://doi.org/10.55730/1300-0098.3361
Available at: https://journals.tubitak.gov.tr/math/vol47/iss1/20