Spacelike Graphs with Parallel Mean Curvature in Pseudo-Riemannian Product Manifolds

• 作 者: Zicheng ZHAO
• 机 构: School of Mathematical Sciences
• 出 处: 数学年刊B辑（英文版）
• 发表日期: 2004年期
• 关键词: Product manifold Spacelike graph Parallel mean curvature Maximal Bernstein

The author introduces the w-function defined on the considered spacelike graph M.Under the growth conditions w =o(log z) and w =o(r),two Bernstein type theorems for M in Rmn+m are got,where z and r are the pseudo-Euclidean distance and the distance function on M to some fixed point respectively.As the ambient space is a curved pseudoRiemannian product of two Riemannian manifolds (∑1,g1) and (∑2,g2) of dimensions n and m,a Bernstein type result for n =2 under some curvature conditions on ∑1 and ∑2 and the growth condition w =o(r) is also got.As more general cases,under some curvature conditions on the ambient space and the growth condition w =o(Υ) or w =o(√Υ),the author concludes that if M has parallel mean curvature,then M is maximal.