Classification of spacelike conformal Einstein hypersurfaces in Lorentzian space Rn+1 1

Yayun Chen, Tongzhu Li*

*此作品的通讯作者

科研成果: 期刊稿件文章同行评审

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
页(从-至)23247-23271
页数25
期刊AIMS Mathematics
8
10
DOI
出版状态已出版 - 2023

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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