Biharmonic PNMCV submanifolds in Euclidean 5-space

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 .