摘要
Let f: Mn → Rn+1 1 be an n-dimensional umbilic-free spacelike hypersurface in the (n + 1)-dimensional Lorentzian space Rn+1 1 with an induced metric I. Let I I be the second fundamental form and H the mean curvature of f. One can define the conformal metric g =n n−1(∥I I∥2 − nH2)I on f (Mn), which is invariant under the conformal transformation group of Rn+1 1. If the Ricci curvature of g is constant, then the spacelike hypersurface f is called a conformal Einstein hypersurface. In this paper, we completely classify the n-dimensional spacelike conformal Einstein hypersurfaces up to a conformal transformation of Rn+1 1.
源语言 | 英语 |
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页(从-至) | 23247-23271 |
页数 | 25 |
期刊 | AIMS Mathematics |
卷 | 8 |
期 | 10 |
DOI | |
出版状态 | 已出版 - 2023 |
指纹
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Chen, Y., & Li, T. (2023). Classification of spacelike conformal Einstein hypersurfaces in Lorentzian space Rn+1 1. AIMS Mathematics, 8(10), 23247-23271. https://doi.org/10.3934/math.20231182