| 张远征.光锥上完备类空超曲面的Calabi-Bernstein问题[J].数学年刊A辑,2025,46(4):435~448 |
| 光锥上完备类空超曲面的Calabi-Bernstein问题 |
| Calabi-Bernstein Problems of Complete Spacelike Hypersurfaces on the Light Cone |
| Received:April 06, 2025 Revised:December 16, 2025 |
| DOI：10.16205/j.cnki.cama.2025.0027 |
| 中文关键词: 类空超曲面 广义极大原理 上光锥 |
| 英文关键词:Spacelike hypersurface Generalized maximum principle Upper light cone |
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| 中文摘要: |
| 设M?为Lorentz-Minkowski时空L??2中落在上光锥上的类空子流形，f为由类光向量或单位类空向量所定义的M?上的仿射函数。在f≠0处，该文用f及其Hessian建立了类空子流形的基本方程。作为应用，在常纯量曲率的条件下,利用广义极大原理证明了：夹在两个同侧平行类光超平面（或类时超平面）之间的光锥上具常纯量曲率的完备类空超曲面只能是平坦空间（或伪球面）。 |
| 英文摘要: |
| Let Mn be a spacelike submanifold in the Lorentz-Minkowski spacetime Ln+2 that lies on the upper light cone, and let f be an affine function on Mn defined by a null vector or a unit spacelike vector. When f ≠ 0, the author establishes the basic equations for spacelike submanifold in terms of f and its Hessian. As an application, the author shows by applying the generalized maximum principle that the flat spaces (or pseudo-spheres) are the only complete spacelike hypersurfaces of the light cone with constant scalar curvature which is between two co-side parallel null hyperplanes (or timelike hyperplanes). |
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