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 $\mathbb{E}^5$.

Keywords: Biharmonic submanifolds, biconservative submanifolds, parallel normalized mean curvature vectors

Full Text: PDF