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| Spacelike Graphs with Parallel Mean Curvature in Pseudo-Riemannian Product Manifolds |
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Citation： |
Zicheng ZHAO.Spacelike Graphs with Parallel Mean Curvature in Pseudo-Riemannian Product Manifolds[J].Chinese Annals of Mathematics B,2012,33(1):17~32 |
| Page view： 2885
Net amount： 2103 |
Authors： |
Zicheng ZHAO; |
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| Abstract： |
The author introduces the w-function defined on the considered spacelike graphM. Under the growth conditions w = o(log z) and w = o(r), two Bernstein type theoremsfor M in Rn+mm are got, where z and r are the pseudo-Euclidean distance and the distancefunction on M to some fixed point respectively. As the ambient space is a curved pseudo-Riemannian product of two Riemannian manifolds (Σ1, g1) and (Σ2, g2) of dimensions nand m, a Bernstein type result for n = 2 under some curvature conditions on Σ1 and Σ2and the growth condition w = o(r) is also got. As more general cases, under some curvatureconditions on the ambient space and the growth condition w = o(r) or w = o(√r), theauthor concludes that if M has parallel mean curvature, then M is maximal. |
Keywords： |
Product manifold, Spacelike graph, Parallel mean curvature, Maximal,Bernstein |
Classification： |
53C42,53C50 |
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