Vol. 300, No. 1, 2019

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Spacelike hypersurfaces with constant conformal sectional curvature in $\mathbb{R}^{n+1}_1$

Xiu Ji, Tongzhu Li and Huafei Sun

Vol. 300 (2019), No. 1, 17–37
Abstract

Let f : Mn 1n+1 be an n-dimensional umbilic-free spacelike hypersurface in the (n+1)-dimensional Lorentzian space 1n+1. One can define the conformal metric g on f which is invariant under the conformal transformation group of 1n+1. We classify the n-dimensional spacelike hypersurfaces with constant sectional curvature with respect to the conformal metric g when n 3. Such spacelike hypersurfaces are obtained by the standard construction of cylinders, cones or hypersurfaces of revolution over certain spirals in the 2-dimensional Lorentzian space forms S12(1),12,1+2, respectively.

Keywords
conformal metric, conformal sectional curvature, conformal second fundamental form, curvature-spiral
Mathematical Subject Classification 2010
Primary: 53A30, 53B25
Milestones
Received: 11 April 2017
Revised: 16 May 2018
Accepted: 9 September 2018
Published: 20 July 2019
Authors
Xiu Ji
Department of Mathematics
Beijing Institute of Technology
Beijing
China
Tongzhu Li
Department of Mathematics
Beijing Institute of Technology
Beijing
China
Huafei Sun
Beijin Key Laboratory on MCAAI
Beijing
China