Para Blaschke isoparametric spacelike hypersurfaces in Lorentzian space forms

2017/02/19 by Xiu Ji, Ji, Xiu, Tongzhu Li +3
Mathematics · Physics and Astronomy · #Advanced Differential Geometry Research #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #math.DG

paper · pdf · doi:10.48550/arxiv.1702.05690

All comments are welcome. arXiv admin note: text overlap with arXiv:1511.07621

arxiv created 2017/02/19 · openalex publication_date 2017/02/19 · arxiv updated 2017/02/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let Mⁿ be an n-dimensional umbilic-free hypersurface in the (n+1)-dimensional Lorentzian space form Mⁿ⁺¹₁(c). Three basic invariants of Mⁿ under the conformal transformation group of Mⁿ⁺¹₁(c) are a 1-form C, called conformal 1-form, a symmetric (0,2) tensor B, called conformal second fundamental form, and a symmetric (0,2) tensor A, called Blaschke tensor. The so-called para-Blaschke tensor D^λ=A+λB, the linear combination of A and B, is still a symmetric (0,2) tensor. A spacelike hypersurface is called a para-Blaschke isoparametric spacelike hypersurface, if the conform 1-form vanishes and the eigenvalues of the para-Blaschke tensor are constant. In this paper, we classify the para-Blaschke isoparametric spacelike hypersurfaces under the conformal group of Mⁿ⁺¹₁(c).

Citations

• Dupin Hypersurfaces in Lorentzian Space forms

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