具有不可对角化形状算子的双守恒Lorentz超曲面
On Biconservative Lorentz Hypersurface with non-diagonalizable shape operator
摘要：
本文得到了具有复特征值形状算子的双守恒Lorentz超曲面$E_{1}^{n+1}$的一些性质。证明了$E_{1}^{n+1}$中每个形状算子具有至多5个不同主曲率的复特征值的双保守Lorentz超曲面$M_{1}^{n}$都具有常数中曲率.另外，我们还研究了具有六个不同主曲率的第二基本型的等长超曲面。
英文摘要：
In this paper, we obtain some properties of biconservative Lorentz hypersurface $M_{1}^{n}$ in $E_{1}^{n+1}$ having shape operator with complex eigen values. We prove that every biconservative Lorentz hypersurface $M_{1}^{n}$ in $E_{1}^{n+1}$ whose shape operator has complex eigen values with at most five distinct principal curvatures has constant mean curvature. Also, we investigate such type of hypersurface with constant length of second fundamental form having six distinct principal curvatures.
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