论文标题
恒定曲率空间中的高空曲面满足特定的圆形型方程
Hypersurfaces in spaces of constant curvature satisfying a particular Roter type equation
论文作者
论文摘要
我们研究了在（n+1）二维的半含量曲率空间n> 3的（n+1）二维半摩恩良好空间中，使操作员A^3（a是m的形状操作员）是操作员A^2和A和身份操作员ID的线性组合。 The main result states that on the set U of all points of M at which the square of the Ricci operator of M is not a linear combination of the Ricci operator and the identity operator, the Riemann-Christoffel curvature tensor R of M is a linear combination of some Kulkarni-Nomizu products formed by the metric tensor g, the Ricci tensor S and the tensor S^2 of m，即张量R可以满足u的某些转子型方程。此外，（0,4）-tensor r.s在u上是由张量G，S和S^2形成的一些速度张量的线性组合。特别是，如果m是一个超浮标，则浸入（n+1）维二维的riemannian恒定弯曲空间，n> 3，具有三个不同的主要曲率和三个独特的特征值，然后是三个不同的特征值，则riemann-christoffel曲率曲率也可以满足这种形式的类型等方程。
We investigate hypersurfaces M isometrically immersed in an (n+1)-dimensional semi-Riemannian space of constant curvature, n > 3, such that the operator A^3, where A is the shape operator of M, is a linear combination of the operators A^2 and A and the identity operator Id. The main result states that on the set U of all points of M at which the square of the Ricci operator of M is not a linear combination of the Ricci operator and the identity operator, the Riemann-Christoffel curvature tensor R of M is a linear combination of some Kulkarni-Nomizu products formed by the metric tensor g, the Ricci tensor S and the tensor S^2 of M, i.e., the tensor R satisfies on U some Roter type equation. Moreover, the (0,4)-tensor R.S is on U a linear combination of some Tachibana tensors formed by the tensors g, S and S^2. In particular, if M is a hypersurface isometrically immersed in the (n+1)-dimensional Riemannian space of constant curvature, n > 3, with three distinct principal curvatures and the Ricci operator with three distinct eigenvalues then the Riemann-Christoffel curvature tensor R of M also satisfies a Roter type equation of this kind.
