Biconservative PNMCV surfaces in the arbitrary dimensional Minkowski space
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In this article, we study biconservative surfaces with parallel normalized mean curvature vector field in the arbitrary dimensional Minkowski space $\mathbb{E}^m_1$, where $m\geq 4$. Firstly, we obtain some geometric properties of these surfaces. In particular, we prove that if $M$ is a PNMCV biconservative surface in $\mathbb{E}^m_1$, then it must be contained in a 4-dimensional non-degenerated totally geodesic of $\mathbb{E}^m_1$ and all its shape operators are diagonalizable. Then, we give local classification theorems for biconservative PNMCV space-like and time-like surfaces in $\mathbb{E}^4_1$.
Abstract
In this article, we study biconservative surfaces with parallel normalized mean curvature vector field in the arbitrary dimensional Minkowski space $\mathbb{E}^m_1$, where $m\geq 4$. Firstly, we obtain some geometric properties of these surfaces. In particular, we prove that if $M$ is a PNMCV biconservative surface in $\mathbb{E}^m_1$, then it must be contained in a 4-dimensional non-degenerated totally geodesic of $\mathbb{E}^m_1$ and all its shape operators are diagonalizable. Then, we give local classification theorems for biconservative PNMCV space-like and time-like surfaces in $\mathbb{E}^4_1$.