Biharmonic PNMCV submanifolds in Euclidean 5-space

Authors

RÜYA ŞEN
NURETTİN CENK TURGAY

DOI

10.55730/1300-0098.3361

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 $\mathbb{E}^5$.

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