BICONSERVATIVE PNMCV SURFACES IN THE ARBITRARY DIMENSIONAL MINKOWSKI SPACE

BICONSERVATIVE PNMCV SURFACES IN THE ARBITRARY DIMENSIONAL MINKOWSKI SPACE

In this article, we study biconservative surfaces with parallel normalized mean curvature vector field in the arbitrary dimensional Minkowski space 𝔼^m₁, where m ≥ 4. Firstly, we obtain some geometric properties of these surfaces. In particular, we prove that if M is a PNMCV biconservative surface in 𝔼^m₁, then it must be contained in a 4-dimensional non-degenerated totally geodesic of 𝔼^m₁ and all its shape operators are diagonalizable. Then, we give local classification theorems for biconservative PNMCV space-like and time-like surfaces in 𝔼⁴₁.