Biharmonic PNMCV submanifolds in Euclidean 5-space

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.